Factors

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

Written by Prerit Jain

Updated on: 15 Feb 2023

Contents

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

## Factors of 138

Factors of 138 | Factor Pairs of 138 | Prime 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**

Looking to Learn Math? Book a Free Trial Lesson and match with top Math Tutors for concepts, homework help, and test prep.

## 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

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

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)

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).

Looking to Learn Math? Book a Free Trial Lesson and match with top Math Tutors for concepts, homework help, and test prep.

## 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 by

Prerit Jain