Factors

# Factors of 132 | Prime Factorization of 132 | Factor Tree of 132

Written by Prerit Jain

Updated on: 15 Feb 2023

Contents

### Factors of 132 | Prime Factorization of 132 | Factor Tree of 132

## Factors of 132

Factors of 132 | Factor Pairs of 132 | Prime factors of 132 |

1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66 and 132 | (1, 132), (2, 66), (3, 44), (4, 33), (6, 22), and (11, 12) | 2 × 2 × 3 × 11. |

Calculate Factors of

**The Factors are**

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## What are the factors of 132

The factors of 132 are numbers that can divide the number 132 without leaving a remainder. To find them out you need to start by dividing 132 by 1 and keep going until you reach its own value:132! There is no magical formula or hacks here—the only way to list each factor for any given number requires patience as well as some basic Math skills. Thus, after division, we have determined these 12 distinct factors of 132 which are (1-12): 1, 2, 3,4,6,8 11., 22., 24 .33 44 66 & Lastly –132 itself!

## How to Find Factors of 132

Through the following methods we can find the factors of 132:

- Factor of 132 using Multiplication Method
- Factors of 132 using Division Method
- Prime Factorization of 132
- Factor tree of 132

## Factors of 132 using Multiplication Method

To discover the factors of 132 using multiplication, start by writing down your number. Next think of two numbers that when multiplied together to get the original number: for example with 132 it would be 1 and 132. Keep going in this way until you have found all the factor pairs–you will eventually come to see that these are (1,132), (2,66), (3,44),(6, 22).

## Factors of 132 Using Division Method

Do you ever wonder how to figure out the factors of a number? Well, if we won’t find what two numbers multiply together to get 132 – known as finding its factor or ‘factors’ – then we can use something called “The Division Method.”

First off it is important to remember that prime numbers are any positive whole number greater than 1 whose only factors (or divisors) are itself and one. So for example 2, 3,5 7, etc… For our purposes here with figuring out the factors of 132 using the division method – first, take square root which in this case gives us 11.5 Then pick the smallest prime number less than 11-which would be 2 & that’s where will start! Divide 132 by two & the remainder should equal 0! That means that ‘2’ is indeed a factor so let’s divide again with the same starting point =132/2= 66 /remainder still equals zero …now 33 comes up making 33 other parts of the equation! From there continue the process of dividing each time until end result ends up being no remainder but instead true factoring…so in our case, the next step was going smallest prime #3 continues steps before…and lo behold 56w/0 remainder meaning both 56&3 became parts of factor equation therefore when multiplied together become final answer–Factors Of 32 Are: 6 X 22.

## Prime Factorization of 132

Calculate Prime Factors of

The Prime Factors of 132 =

2 x

2 x

3 x

11

Do you ever wonder how a number like 132 can be expressed in terms of prime numbers? It’s not as hard as it seems! To find the prime factorization for 132, first, we divide by 2 (the smallest prime less than or equal to its square root). Then, keep dividing that result until there are no more whole-number solutions. In this case, our two factors were 66 and 33 – combining those gives us 132 again! Fifth graders: try following these steps with any other huge-looking numbers if you need help understanding better!

## Factor tree of 132

Let’s explore how we can find all the prime factors of 132, a number that is larger than 100! To do this, we will use factor trees. Factor trees help us identify all the different prime numbers that go into making up a bigger number like 132. Here are our steps: First divide 132 by 2—the smallest possible prime less than 11.5 (which is approximately equal to its square root). We get 66 with no remainder which means 2 goes into 132 exactly once and thus it’s one of our factors! Then take your result from before (66) and try dividing again -this time by 3- you’ll end up getting 33 with 0 leftover meaning 3 also divides evenly in to make another one of our needed factorials for figuring out what makes up anything close or greater than 100; keep repeating this process until there are no longer any even divisions made between your starting number (132), smaller primes(2/3/4, etc.) resulting in every single factor being discovered successfully.

## Factor Pairs of 132

Calculate Pair Factors of

1 x 132=132

2 x 66=132

3 x 44=132

4 x 33=132

6 x 22=132

11 x 12=132

12 x 11=132

22 x 6=132

33 x 4=132

44 x 3=132

66 x 2=132

So Pair Factors of 132 are

(1,132)

(2,66)

(3,44)

(4,33)

(6,22)

(11,12)

(12,11)

(22,6)

(33,4)

(44,3)

(66,2)

Learning factor pairs of a number can be an exciting and engaging experience. To show you how to let’s use the example of 132! We’ll start by writing out all its factors in order from smallest to largest – 1, 2, 3, 4, 6 8 11 12 22 33 44 66, and 132. Then we pair up these numbers two at a time starting with the small ones (1 &2) on till we reach the biggies(66&132). This gives us each combination as a ‘factor pair’ like (1/132),(2/66), etc which for our particular case would look something like this:

(1-132),

(2-67),

(3–44).

etc. It is important to remember that even if you change the position or sides inside each equal sign – it will still give the same answer no matter what!. So try switching places between 4 &33 so they become 133 while solving challenges involving such equations!

## Factors of 132 – Quick Recap

**Factors of 132:** 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, and 132.

**Negative Factors of 132:** -1, -2, -3, -4, -6, -11, -12, -22, -33, -44, -66, and -132.

**Prime Factors of 132: **2 × 2 × 3 × 11

**Prime Factorization of 132:** ** **2 × 2 × 3 × 11

## Fun Facts of Factors of 132

Fascinating!

- 132 is an interesting number because it can be separated into 14 parts. That’s quite a few, making the possibilities for expressing this composite number as the product of two or more integers virtually endless.
- Not only that – when you add up all its factors (except itself), they’ll total 264; and if you multiply them? 1344!

## Examples of Factor of 132

**1. Tom has 132 marbles and wants to share them evenly among 8 children. How many marbles will each child get?**

**Answer:** Each child will get 16 marbles (132 / 8 = 16).

**2. Bob needs to buy 132 items from a store that only accepts payment in multiples of seven dollars up to 25 dollars maximum per purchase transaction. How few transactions must Bob make? **

**Answer: **Bob must make 13 transactions (7 x 19 = 133; 133 – 132 = 1 which is less than the maximum purchase transaction of 25).

**3. Carla purchased an item that cost $132, but she only had two $50 bills and coins. How much change did she receive? **

**Answer: **Carla received $32 in change ($50 + $50 = $100; $100 – $132 = -$32; -$32 + $32 = 0).

**4. What is the greatest common factor of 26 and 132?**

**Answer:** The greatest common factor of 26 and 132 is 2 (26÷2=13; 132÷2=66; 66÷2=33; 33÷3=11 ).

**5. Jane needs to divide 132 slices of pizza equally among 23 people. How many slices will each person get? **

**Answer:** Each person will get 5 slices of pizza (132 / 23 = 5).

**6. What is the least common multiple of 26 and 132? **

**Answer: **The least common multiple of 26 and 132 is 612 (26 x 24 = 624; 624 ÷ 2=312; 312 x 11=3432; 3432 ÷ 11 = 312; 312 ÷ 2= 156; 156 ÷ 3=52; 52 x 11=572; 572 ÷ 7=82; 82 x 7=574; 574-612=-38).

**7. Joe needs to buy 12 items that cost eight dollars each and eight items that cost nine dollars each from a store that only accepts payment in multiples of nine dollars up to 45 dollars maximum per purchase transaction. How many transactions must Joe make to buy all 20 items? **

**Answer: **Joe must make three transactions in order to buy all 20 items (9 x 12 = 108, 9 x 8 = 72, 108 + 72 + 4 (remainder) = 184, 184/9 =20 with 4 remaining cents which are less than 45).

**8. Find two consecutive numbers whose product is a factor of 132. **

**Answer:** The two consecutive numbers are 11 and 12 since their product, 132, is a factor of 132 (11×12=132).

**9. Express 132 as a product of its prime factors. **

**Answer:** The prime factors for 132 are 2 X 2 X 3 X 11 or 22 X 3 X 11 where 2 appears twice so it can be expressed as 22 X 3 X 11.

**10. Can 132 be evenly divided by 3? By 7? By 11? Answers: **Yes, 132 can be evenly divided by 3, 7, and 11 ([132/3] remainder 0; [132/7] remainder 0 ; [132/11] remainder 0 ).

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## Frequently Asked Questions on Factors of 132

**What are the factors of 132?**

The factors of 132 are 1, 2, 3, 4, 6, 11, 12, 13, 22, 26, 33, 44, 66, and 132.

**Is 132 a prime number?**

No, 132 is not a prime number because it has more than two factors.

**What is the greatest common factor of 13 and 132?**

The greatest common factor of 13 and 132 is 1.

**What is the least common multiple of 13 and 132?**

The least common multiple of 13 and 132 is 612.

**Express 132 as a product of its prime factors. **

The prime factors for 132 are 2 X 2 X 3 X 11 or 22 X 3 X 11 where 2 appears twice so it can be expressed as 22 X 3 X 11.

**Determine whether 132 is a square number, a cube number, or neither.**

Neither; 172 is not a square number nor a cube number since its square root (11 . 567) does not have an integer value nor does its cube root(4 . 743).

**Can 132 be evenly divided by 3? By 7? By 11?**

Yes; 132 can be evenly divided by 3, 7, and 11 ([132/3] remainder 0; [132/7] remainder 0 ; [132/11] remainder 0 ).

**Find two consecutive numbers whose product is a factor of 132.**

The two consecutive numbers are 11 and 12 since their product,132, is a factor of 132 (11×12=132).

**Find the largest factor of 132.**

The largest factor of 132 is 132 itself (132 ÷ 1 = 132).

**Find the smallest factor of 132.**

The smallest factor of 132 is 1 (1 x 132 =132 ).

Written by

Prerit Jain