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Factors

Factors of 138 | Prime Factorization of 138 | Factor Tree of 138

Written by Prerit Jain

Updated on: 15 Feb 2023

Contents

1Factors of 12Factors of 23Factors of 34Factors of 45Factors of 56Factors of 67Factors of 78Factors of 89Factors of 910Factors of 1011Factors of 1112Factors of 1213Factors of 1314Factors of 1415Factors of 1516Factors of 1617Factors of 1718Factors of 1819Factors of 1920Factors of 2021Factors of 2122Factors of 2223Factors of 2324Factors of 2425Factors of 2526Factors of 2627Factors of 2728Factors of 2829Factors of 2930Factors of 3031Factors of 3132Factors of 3233Factors of 3334Factors of 3435Factors of 3536Factors of 3637Factors of 3738Factors of 3839Factors of 3940Factors of 4041Factors of 4142Factors of 4243Factors of 4344Factors of 4445Factors of 4546Factors of 4647Factors of 4748Factors of 4849Factors of 4950Factors of 5051Factors of 5152Factors of 5253Factors of 5354Factors of 5455Factors of 5556Factors of 5657Factors of 5758Factors of 5859Factors of 5960Factors of 6061Factors of 6162Factors of 6263Factors of 6364Factors of 6465Factors of 6566Factors of 6667Factors of 6768Factors of 6869Factors of 6970Factors of 7071Factors of 7172Factors of 7273Factors of 7474Factors of 7575Factors of 7676Factors of 7777Factors of 7878Factors of 7979Factors of 8080Factors of 8181Factors of 8282Factors of 8383Factors of 8484Factors of 8585Factors of 8686Factors of 8787Factors of 8888Factors of 8989Factors of 9090Factors of 9191Factors of 9292Factors of 9493Factors of 9694Factors of 9795Factors of 9896Factors of 9997Factors of 10098Factors of 10199Factors of 102100Factors of 103101Factors of 104102Factors of 105103Factors of 106104Factors of 107105Factors of 108106Factors of 109107Factors of 110108Factors of 111109Factors of 112110Factors of 113111Factors of 114112Factors of 115113Factors of 116114Factors of 117115Factors of 118116Factors of 119117Factors of 120118Factors of 122119Factors of 123120Factors of 124121Factors of 125122Factors of 126123Factors of 127124Factors of 128125Factors of 129126Factors of 130127Factors of 131128Factors of 132129Factors of 133130Factors of 134131Factors of 135132Factors of 136133Factors of 137134Factors of 138135Factors of 139136Factors of 140137Factors of 141138Factors of 142139Factors of 143140Factors of 144141Factors of 145142Factors of 146143Factors of 147144Factors of 148145Factors of 149146Factors of 150147Factors of 151148Factors of 152149Factors of 153150Factors of 154151Factors of 155152Factors of 156153Factors of 157154Factors of 158155Factors of 159156Factors of 160157Factors of 161158Factors of 162159Factors of 163160Factors of 167161Factors of 168162Factors of 169163Factors of 170164Factors of 172165Factors of 174166Factors of 176167Factors of 178168Factors of 180169Factors of 182170Factors of 184171Factors of 186172Factors of 188173Factors of 190174Factors of 192175Factors of 194176Factors of 196177Factors of 197178Factors of 200179Factors of 215180Factors of 216181Factors of 415
Factors of 138 | Prime Factorization of 138 | Factor Tree of 138

Factors of 138 | Prime Factorization of 138 | Factor Tree of 138

Factors of 138

Factors of 138Factor Pairs of 138Prime factors of 138
1, 2, 3, 6, 23, 46, 69, 138(1, 138), (2, 69), (3, 46), (6, 23)2 × 3 × 23

Calculate Factors of

The Factors are

https://wiingy.com/learn/math/factors-of-138/

What are the factors of 138

To understand the factors of 138, picture it as a matching game: For every number from 1 to 138 that divides evenly into 138, you get one card in your hand. The goal is for each card in your hand to find its “pair” – another number that can be multiplied with yours so they both equal exactly 138! This means when you have 2, 69 should divide out perfectly giving us (2 & 69) as our first factor pair of this exciting mental math adventure! Going through all numbers until we reach the square root – any divisors found along this journey create other even pairs and will help identify all the factors of “138”!

How to Find Factors of 138

The following methods help to find the factors of 138:

  • Factor of 138 using Multiplication Method
  • Factors of 138 using Division Method
  • Prime Factorization of 138
  • Factor tree of 138

Factors of 138 using Multiplication Method

All you need is a set of two numbers that when multiplied together gives the original number.
For example,
Here, we have 1×138 = 138 and 2 x 69 = 138 – see how they both come up to our number! This works all the way down until 9 x 18 = 138 which means that each one of those pairs gives us a factor: 1, 2, 3, 6,9,18, 23 46 & 69 respectively.

Factors of 138 Using Division Method

To find the factors of 138 using division, 

  • Start by dividing it by its smallest divisor – 1. 
  • If you continue to divide that number with increasing values (2, 3, etc.), eventually each result will be a factor of the original number when multiplied together. 
  • This method is an effective way to identify all possible factors for any given value. When applied to 138, this technique reveals that there are 9 different sets of numbers that form multiples producing138 as their sum: 1 x 138; 2 x 69; 3 x 46; 6 x 23;9x 18;18x 9;23×6,46×3, and finally 69X2.

Each set provides one factor from either side totaling up in combination towards creating 138!

Prime Factorization of 138

Calculate Prime Factors of

The Prime Factors of 138 =

2 x

3 x

23

https://wiingy.com/learn/math/factors-of-138/

Students can find the prime factorization of any number by first dividing it by the smallest prime number, then continuing to divide that result in turn with each subsequent smaller prime number until they reach a point where division no longer yields a whole number.

For example: To work out the Prime Factorization of 138 we start by dividing it by 2; this gives us 69 which is not an integer so we continue on and divide 690 again by 2 (34.5). As 34.5 isn’t an integer either, our next step would be to move onto 3 – thus 1/3 being 46- before finally moving onto 5 when nothing else works under those parameters anymore giving us 15 as our answer!

Factor tree of 138

138269323
https://wiingy.com/learn/math/factors-of-138/

To understand factor trees, 

  • Let’s start by breaking down what a prime number is – it’s an integer that can only be divided evenly by one and itself. So when looking at the number 138, we will note its two smallest prime factors: 2 and 3. 
  • If you divide these numbers into each other until there are no more integers left to divide (known as “prime decomposition”), this process of finding all the possible combinations of those individual primes within larger numbers forms your equation tree! 
  • When completed for 138 in our example above, you’ll see how every combination ultimately leads back to getting exactly equal parts which add up together again – resulting in your original starting point being accurately represented on the chart.

Factor Pairs of 138

Calculate Pair Factors of

1 x 138=138

2 x 69=138

3 x 46=138

6 x 23=138

23 x 6=138

46 x 3=138

69 x 2=138

So Pair Factors of 138 are

(1,138)

(2,69)

(3,46)

(6,23)

(23,6)

(46,3)

(69,2)

https://wiingy.com/learn/math/factors-of-138/

Factor pairs are groups of integers (whole numbers) that when multiplied together give you a specific number. To use 138 as an example, its factor pair includes 1 and 138; 2 and 69; 3 and 46; 6 and 23; 9 and 18. By dividing any given number by each successive divisor up until it reaches its own square root–in this case 13 for 138–students can utilize basic division skills in order to determine which set of integer combinations from these divisions would result in their target value:138!

Factors of 138 – Quick Recap

Factors of 138: 1, 2, 3, 6, 23, 46, 69, 138.

Negative Factors of 138: -1, -2, -3, -6, -23, -46, -69, -138.

Prime Factors of 138:2 × 3 × 23

Prime Factorization of 138:  2 × 3 × 23

Fun Facts of Factors of 138

  • 138 may be an even number, but it’s also a composite one – meaning that its factors are more complex than just two (which is usually the case with prime numbers). 
  • To understand what makes up 138 and all of its individual components we have to look at something known as prime factorization. 
  • Prime Factorization breaks down any given number into the ‘building blocks which lead up to making them – in this instance, those building blocks would be 2 x 3 x 23! Combining these together gives us 1, 2, 3, 6,23 46 69 & 138 making 272 when added together. What’s interesting here though isn’t only how many combinations you can get from combining these elements; it’s that factoring out sums 262 itself results back in our original figure:138. 

Examples of Factor of 138

1. What is the greatest common factor of 138 and 27?

Answer: The greatest common factor (GCF) of 138 and 27 is 3 (3×3=9).

2. How many groups of 6 can be formed if you have 138 items?

Answer: You can form 23 groups with 6 items each if you have 138 items (138 ÷ 6 = 23).

3. If Robert has 137 coins, how many quarters will he have? 

Answer: Robert will have 53 quarters if he has 137 coins (137 x

0.25 =34.25, round down to 34 and then multiply by 4 to get 136, adding an extra quarter equals 53).

4. What is the least common multiple of 25 and 138? 

Answer: The least common multiple (LCM) of 25 and 138 is 6900 (25 x 138 = 3500, which can be divided by 2 to get 1750, then divided by 5 to get 350, then divided by 10 to get 70, and finally by 5 again to get 14).

5. If 158 oranges are divided into groups of 11, how much will each group receive? 

Answer: Each group will receive 14 oranges if 158 oranges are divided into groups of 11 (158 ÷ 11 = 14 with the remainder 4).

6. Find the prime factors for the number 138 using exponential notation for any prime factors that appear more than once in the factor tree. 

Answer: The prime factors for 138 using exponential notation are 2 x 3² x 23 or 2⁰ x 3² x 23. 
      .7. How many pairs of 32 do you need for a total sum of 138?
Answer: You need 4 pairs of 32 for a total sum of 138(32×4=128, add another ten equals 138). 

8. If Arthur sells 43 shoes at $7 each, how much money does he make?
Answer: Arthur makes $301selling 43 shoes at $7each($7×43=301 ).  

9. If I divide 142 into groups of 12, how many groups will I have leftover?
Answer: You will have 3 groups left over if you divide 142 into groups of 12 (142÷12=11withremainder10 ).  

10. What two numbers can you multiply together to get the product 133?
Answer:
You can multiply 67×2 or 17×7 to get the product133(67×2=134 ,17×7=119).

Frequently Asked Questions on Factors of 138

What are the factors of 138?

The factors for 138 are 1, 2, 3, 6, 23, 34, 46, 69, and 138.

What is the greatest common factor for 138?

The greatest common factor (GCF) for 138 is 3 (3×3=9).

What is the least common multiple of 25 and 138?

The least common multiple (LCM) of 25 and 138 is 6900 (25 x 138 = 3500, which can be divided by 2 to get 1750, then divided by 5 to get 350, then divided by 10 to get 70, and finally by 5 again to get 14).

How many groups of 6 can be formed if you have 138 items?

You can form 23 groups with 6 items each if you have 138 items(138÷6=23).

How many pairs of 32 do you need for a total sum of 138?

You need 4 pairs of 32 for a total sum of 138 (32×4=128, add another ten equals 138).

If 158 oranges are divided into groups of 11, how much will each group receive?

Each group will receive 14 oranges if 158 oranges are divided into groups of 11(158÷11=14with remainder 4).

Find the prime factors for the number 138 using exponential notation for any prime factors that appear more than once in the factor tree.

The prime factors for 138 using exponential notation are 2×3²x23or2⁰x3²x23

What two numbers can you multiply together to get the product133?

You can multiply 67×2 or 17×7 to get the product 133(67×2=134,17×7=119).

If Arthur sells 43 shoes at $7 each, how much money does he make?

Arthur makes $301selling 43 shoes at $ 7 each ($7×43=301 ).

If I divide 142 into groups of 12, how many groups will I have left over?

You will have 3 groups left over if you divide 142 into groups of 12 (142÷12=11with remainder10 ).

Written by

Prerit Jain

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