Factors

# Factors of 168 | Prime Factorization of 168 | Factor Tree of 168

Written by Prerit Jain

Updated on: 12 Aug 2023

Contents

### Factors of 168 | Prime Factorization of 168 | Factor Tree of 168

Factors of 168 | Factor Pairs of 168 | Prime factors of 168 |
---|---|---|

168 = 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, and 168. | (1, 168), (2, 84), (3, 56), (4, 42), (6, 28), (7, 24), (8, 21) and (12, 14). | 168= 2 × 2 × 2 × 3 × 7 |

**What are the factors of 168**

Calculate Factors of

**The Factors are**

**Draft 1**

Don’t you know what the factors of 168 are? Factors are numbers multiplied together to create a bigger number. To find out all the factors for 168, we need two tools: Dividing and Prime Factorization! Let’s use both of them on our journey through math!!

Dividing is when we divide one big number: 168 by another smaller whole integer between 1 and 16. Consider dividing it with 2, 3 or 4…If any result comes out with no number left behind then they become one of the factors – these integers will multiply together fitting perfectly into our original number. The results obtained using this method were 1,2 ,3 ,4 , 6, 7 8 12 14 21 24 28 42 56 84 & 168 .Such an impressive result it appears. Now about prime factorisation; It helps in finding detailed information behind each answer mentioned above- Every single result from the divisible test was made up from only two components : A multiple form of 2s’and of 7s’. As long as the combined efforts of primes is there it brings Numerical perfection (i.e) perfect combination.

**How to Find Factors of 168**

**Draft 1**

The four proven methods that you can use to find the factors of 124:

Factor of 124 using Multiplication Method

Factors of 124 using Division Method

Prime Factorization of 124

Factor tree of 124

**Factors of 168 using Multiplication Method**

**Draft 1**

To find the factors of 168, we use a multiplication method called dividing without any remainders (i.e) that if you divide 168 by an integer between 1 and 168, it will divide with no remainder. Then when each factor of 169 is multiplied together it should result in the original number (168) , say, 1 x 2 x 3 x 4 = 24; 24x 7=168… Another such example is – 8 × 12 × 14 = 2016 which also equals our starting point – 168 – proving these three numbers can go into 168 evenly. Other possible combinations are 1,2,3 ,4, 6,7,8,12,14, 21,24, 28, 42, 56, 84 or even all sixteen combined at once : 1×2×3×4…. So these sixteen are the ‘factors of 168.

**Factors of 168 Using Division Method**

**Draft 1**

Dividing is the best way to find out the factors of 168! because when we divide this number, we’re asking “what numbers can be used to make up 168?”. So if you want to know what those numbers are – they are 1, 2, 3, 4 ,6 ,7 ,8 12 14 21 24 28 42 56 84 and 168!. All these different figures builds and makes up our original number

**Prime Factorization of 168**

Calculate Prime Factors of

The Prime Factors of 168 =

2 x

2 x

2 x

3 x

7

Prime factorization is breaking down a bigger number into smaller numbers that multiply together to give you the original number. Consider 168, its prime factors are 2x2x2 (aka “to the power of 3”) multiplied by 7. This means that even if the individual pieces of the broken number can be put back together in different ways leading to the original starting point!

**Factor tree of 168**

One fun way to break down any number into its prime factors is factor trees! consider 168. Imagine two branches coming off of this top section where we wrote 168. On each of these branches, write what happens when you divide by 2 twice in a row; so on one branch will be 84 and then 42 on the other branch from that same starting point at 168. Then imagine another pair of branches for each new quotient written in step 3 (84) & 4 (42), both separated again by dividing them all by 2 as before- leaving us with 21 and 1 respectively .Now if you look: You will have 7 little sections branching out like tree limbs . The numbers left are the prime factors; In this case they’re 2 x2x2x3x7 = 168

**Factor Pairs of 168**

Calculate Pair Factors of

1 x 168=168

2 x 84=168

3 x 56=168

4 x 42=168

6 x 28=168

7 x 24=168

8 x 21=168

12 x 14=168

14 x 12=168

21 x 8=168

24 x 7=168

28 x 6=168

42 x 4=168

56 x 3=168

84 x 2=168

So Pair Factors of 168 are

(1,168)

(2,84)

(3,56)

(4,42)

(6,28)

(7,24)

(8,21)

(12,14)

(14,12)

(21,8)

(24,7)

(28,6)

(42,4)

(56,3)

(84,2)

Take the number 168. You’ll need to find all the numbers that can divide it without any remainders called “divisors”. Factor pairs is one of the best ways to do this! This is basically finding two factors which when multiplied together equal our original number – in this case, 168. For example: 1 times 168 would be one pair; 2 and 84 makes another pair; 6 x 28 =168 too. Factor-finding isn’t just limited to multiplying either – other methods such as division or prime factorization can help us discover more combinations.

**Factors of 168 – Quick Recap**

**Factors of 168:** 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, and 168

**Negative Factors of 168:** 1-, -2, -3, -4, -6, -7, -8, -12, -14, -21, -24, -28, -42, -56, -84, and -168.

**Prime Factors of 168:** 2 × 2 × 2 × 3 × 7

**Prime Factorization of 168:** 2 × 2 × 2 × 3 × 7

**Fun Facts of Factors of 168**

168 is special why? Because, this number can do lots of amazing stuffs! If we add together all the cubes from 1 to 4 we get 168. That’s just for starters – there are plenty more interesting facts on the way about this great numeral.

Did you know that out of all whole numbers less than itself, 168 has the most number of divisors? (24) scientists call it a ‘highly composite’ number and amazingly enough when written in base-10 form like our normal counting system ,168 also happens to be Harshad Number meaning all its digits divide into exactly 14 parts!!

Last but not least; due to a high number of factors compared with smaller integers and as their sum equals twice its original value ;we say even today after thousands upon thousands years ,that big old wealthy numeric Duke named “One Hundred Sixty Eight” — HARMONIOUS DIVISOR NUMBER !

**Examples of Factor of 168**

1) If Tim has 168 cards, how many ways can he evenly divide the cards amongst 4 friends?

Answer: Tim can evenly divide the 168 cards into 4 groups of 42 cards each, so that each friend receives an equal amount.

2) Sarah needs to buy 168 pencils for her school. How many pencils does she need to buy for each classroom if there are 8 classrooms in total?

Answer: Sarah needs to buy 21 pencils for each classroom, so that all 8 classrooms are provided with 168 pencils altogether.

3) Brooke has a packet of 168 gummy bears. She wants to give an equal amount of gummy bears to each of her six siblings. How many gummy bears should she give each one?

Answer: Brooke should give 28 gummy bears to each of her siblings, so that all 6 siblings receive an equal amount and also so all 168 gummy bears in the packet are used up accordingly!

4) Paul is playing a game involving dice with 6 players, if they have a total of 168 dice, how many dice will each player get?

Answer: Each player will receive 28 dice from the total of 168 dice available.

5) Jimmy bought three boxes containing 56 items each and another containing 40 items; what is the highest common factor between these numbers?

Answer: The highest common factor between these numbers is 8; as 8 is a factor of 56, 40 and168 when multiplied together or deducted from itself respectively!

6) Kevin wanted to distribute 10 candies equally among his 11 friends but realized he was short 2 candies compared to what was needed for everyone; what would be the other factor besides 10 if he had enough candy?

Answer: The other factor besides 10 that Kevin would need for his friends would be 9; since 9 plus 10 equals 19 candies which is exactly what Kevin needs!

7) Alex was asked by his boss to make 169 ice cubes but made one extra cube by mistake – What is the other factor besides 1 when counting down from 169 if Alex only had enough material for two-thirds of it ?

Answer: The other factor besides 1 when counting down from 169 when Alex only has enough material too two-thirds of it would be 112; as 112 plus 1 equals 113 cubes altogether!

8 ) Rachel needed to fill up 169 balloons but only had enough material available for one-half of it instead – What is the other factor besides 84 Rachel needs in order to fill it up completely ?

Answer: The other factor besides 84 Rachel needs in order fill up all169 balloons would be 85 ; 85 plus 84 being exactly 169 balloons requested !

9) Eric was given 16 bags filled with cards and needed help dividing it equally between 2 people but found out there were actually only 136 cards altogether instead of168 -What is the new factor if 136cards were divided amongst two people instead ? Answer: The newfactorif136cardswere divided amongst two people instead would be 68 ; as 68 plus 68 equals 136cardsaltogether !

10) Grace bought four boxes containing 42 items per box and another containing 24 items; what is the lowest common multiple between these numbers?

Answer: The lowest common multiple between these numbers is 336; as 336 divided once by 42 (or twice by 24), thrice by 28 and four times by 21 results in 1 being its lowest common denominator!

**Frequently Asked Questions**

### What is a factor of 168?

Answer: A factor of 168 are any number that divides into 168 with no remainder. The factors of 168 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 21 ,24 ,28, 36 ,42 ,56 ,63 and 84.

### How many factors does 168 have?

Answer: There are 18 factors of 168.

### How can you find the common factors of two numbers such as 168 and 126?

Answer: To find the common factors of two numbers such as 168 and 126 start by listing out the factors for each number. For 168 these are 1,2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 21, 24, 28, 36, 42, 56, 63, 84. For 126 these are 1, 2 ,3, 6, 9, 18, 27, 39, 54,81. Then cross off any numbers on both lists until there’s nothing left over- these will be your common factors which in this case is 1 and 3.

### What is the highest common factor between 167 (3×58), 162 (3×58+1), 163 (3×58+2), 164 (3×58+3), 165 (3×58+4), 166 (3×58+5) and 167(44)?

Answer: The highest common factor between these numbers is 1; as no prime factors exist between any two numbers except when one number subtracts from itself or else when multiplying it by 1 – resulting in 1 being its highest common denominator!

### How can you evenly divide 169 items into three containers?

Answer: To evenly divide 169 items into three containers you can start by calculating 169 divided by 3 to get a total of 56 items per container. You can then split up the remaining items among the three containers so that each contains an equal amount- in this case 53 items per container.

### What two prime numbers make up168?

Answer: The two prime numbers that make up 168 are 7 and 23 – which when multiplied together give you a result of 168.

### If Mary has 176 apples to distribute equally among 5 people, how many apples will each person receive?

Answer: Each person will receive 35 apples since 176 divided by 5 equals 35 apples for each person.

### Is 167 a prime number?

Answer: No. 167 is not a prime number because its divisors include 1 and 167 which mean it has more than two its own divisors besides itself- making it not qualify as a prime number.

### Does every number have four or more factors?

Answer: No – while most numbers have more than four factors some like 37 only have two while others like 169 only have four total- leading to varying amounts depending on what specific number you’re referencing within this category!

### How many times can 8 be divided into 144 without leaving a remainder ?

Answers : Eight can be divided into 144 eight times without leaving a remainder since 144 ÷ 8 equals 18 with no remainders or fractions left over!

Written by

Prerit Jain