Factors

# Factors of 129 | Prime Factorization of 129 | Factor Tree of 129

Written by Prerit Jain

Updated on: 21 Jun 2023

Contents

### Factors of 129 | Prime Factorization of 129 | Factor Tree of 129

## Factors of 129

Factors of 129 | Factor Pairs of 129 | Prime factors of 129 |

1, 3, 43, 129 | (1, 129), (3, 43) | 3 × 43 |

**Factors of 129**,

**Factor Pairs of 129**,

**Prime factors of 129**

Calculate Factors of

**The Factors are**

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## What are the factors of 129

Understanding factors can be tricky, but with a few simple steps, you’ll have it down pat! To find the factors of 129 we must list all integers from 1 to 129 and then divide them into 128 one by one. If the result is not a remainder (or “leftover” answer), then that number on your list can be called a Factor! In this case, our Factors for 127 are 1, 3, 43 & 129 – try different numbers yourself to see how it works out.

## How to Find Factors of 129

The most significant methods through which we can find the factors of a number are given below and they can also be used to find the factors of 129.

- Factors of 124 using the Multiplication Method
- Factors of 124 using the Division Method
- Prime Factorization of 124
- Factor tree of 124

## Factors of 129 Using the Multiplication Method

To find the factors of 129 using the multiplication method, follow these steps:

- Start with the number 1.
- Multiply 1 by 129 to get 129. This means that 1 and 129 are factors of 129.
- Proceed to the next number, which is 2. Multiply 2 by 64.5, but since the result is not a whole number, it is not a factor.
- Move on to the next number, which is 3. Multiply 3 by 43 to get 129. This means that 3 and 43 are factors of 129.
- Continue this process, checking each number up to the square root of 129, which is approximately 11.36. Since 129 is not divisible by any numbers between 4 and 11, we have found all the factors.

**Therefore, the factors of 129 are 1, 3, 43, and 129.**

## Factors of 129 Using the Division Method

If you want to figure out the prime factorization of a number like 129, it’s easy! Follow this process:

- Start with the number 1.
- Divide 129 by 1. If the division result is a whole number, then 1 is a factor of 129.
- Move on to the next number, which is 2. Divide 129 by 2. If the division result is a whole number, then 2 is a factor of 129.
- Continue this process, checking each number up to the square root of 129, which is approximately 11.36. Divide 129 by each number and check if the division result is a whole number.
- If the division result is a whole number, then the divisor is a factor of 129.
- Once you have checked all the numbers up to the square root of 129, you have found all the factors.

**Therefore, the factors of 129 are 1, 3, 43, and 129.**

## Prime Factorization of 129

Calculate Prime Factors of

The Prime Factors of 129 =

3 x

43

- Start by dividing 129 by the smallest prime number, which is 2. However, 129 is not divisible by 2, so we move on to the next prime number.
- Divide 129 by the next prime number, which is 3. 129 divided by 3 equals 43, with no remainder. So, we have found one prime factor: 3.
- Now, we continue dividing the quotient, which is 43, by prime numbers starting from 2, 3, 5, and so on. However, since 43 is a prime number itself, we cannot divide it any further.
- Therefore, the prime factorization of 129 is 3 * 43.

**To summarize, the prime factorization of 129 is 3 * 43.**

## Factor tree of 129

Let’s explore the process of finding prime factors for numbers by using a factor tree. For example, did you know that if we divide 129 (our number) by 2 or 3, we might get its respective Prime Factors? Starting off it is important to find out what is the square root of our given number. In this case, it’s 11.5; so since 2 and 3 are both smaller than 11.5 they could be potential fractions! When dividing 129 by two there was no ‘remainder’ but when divided by three – 43 came up as a result making ‘3’ one fraction while also indicating another fraction present in 129 which will give us our answer after division i:e 1!

## Factor Pairs of 129

Calculate Pair Factors of

1 x 129=129

3 x 43=129

43 x 3=129

So Pair Factors of 129 are

(1,129)

(3,43)

(43,3)

- Start with the number 1 as a potential factor.
- Divide 129 by 1 to check if it evenly divides. If it does, you have found a factor pair: (1, 129).
- Move on to the next number, which is 2, and repeat the division: 129 ÷ 2 = 64.5 (not a whole number).
- Continue with the next number, which is 3: 129 ÷ 3 = 43. This is a whole number, so you have found another factor pair: (3, 43).
- Keep going with the next numbers until you reach the square root of 129, which is approximately 11.36. After that point, the factors will repeat.

**The factor pairs of 129 are (1, 129) and (3, 43).**

## More Factors

## Factors of 129 – Quick Recap

**Factors of 129:**1, 3, 43, 129**Negative Factors of 129:**-1, -3, -43, and -129**Prime Factors of 129:**3 × 43**Prime Factorization of 129:**

## Solved Examples of Factor of 129

**Q.1: What are the factors of 132?****Solution:**The factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, and 132.

**Q.2:** Is 132 a prime number?** Solution:** No, 132 is not a prime number because it has more than two factors.

**Q.3:** What is the greatest common factor of 13 and 132?** Solution: **The greatest common factor (GCF) of 13 and 132 is 1. Since 13 is a prime number, its only factors are 1 and 13. For 132, its factors include 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, and 132. The highest common factor among these numbers is 1, making it a GCF of 13 and 132.

**Q.4:** What is the least common multiple of 13 and 132? ** Solution: **The least common multiple (LCM) of 13 and 132 is 132. Since 13 is a prime number, it cannot be divided evenly by any number other than 1 and itself. The multiples of 13 are 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, and so on. For 132, the multiples include 132, 264, 396, 528, 660, 792, 924, and so on. The first common multiple between 13 and 132 is 132 itself, as it is divisible by both numbers. Therefore, the LCM of 13 and 132 is 132.

**Q.5:** Express 132 as a product of its prime factors. ** Solution: **The prime factorization of 132 is: 2 × 2 × 3 × 11.

**Q.1:** Determine whether 132 is a square number, a cube number or neither? ** Solution: **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).

**Q.6:** Can 132 be evenly divided by 3? By 7? By 11? **Solution:** 132 is divisible by 3. 132 is not divisible by 7. 132 is divisible by 11.

**Q.7:** Find two consecutive numbers whose product is a factor of 132. ** Solution: **The two consecutive numbers are 11 and 12 since their product,132, is a factor of 132 (11×12=132).

**Q.8:** Find the largest factor of 132. **Solution:** The largest factor of 132 is 132 itself (132 ÷ 1 = 132).

**Q.9:** Find the smallest factor of 132. ** Solution: **The smallest factor of 132 is 1 (1 x 132 =132 ).

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**Frequently Asked Questions on Factors of 129**

**Two friends are sharing candy. If one friend has 129 pieces and the other has 3 pieces, how many times more candy does the first friend have?**

43 times more candy (129 ÷ 3 = 43)

**A school club has 129 members, and they want to divide themselves into groups of 3. How many groups will there be?**

43 groups (129 ÷ 3 = 43).

**Keith needs to print out 129 pages for a project, but his printer can only print 11 pages at a time. How many times will he need to reload the printer paper?**

12 times (129 ÷ 11 = 12).

**A bus has 129 seats and 26 people are boarding it. Is it possible to let everyone board without breaking any seat limits?**

Yes, since 26 is a factor of 129 (129 ÷ 26 = 5).

**Vivian got a cash reward of $129 for winning an award, and she wants to evenly split this money with her best friend Nelly. How much money will each of them get?**

Each of them gets $64.50 ($129 ÷ 2 = 64.50)

**The local swimming pool measures 17 meters long and 7 meters wide, but it needs to be filled with 129 liters of water before people can start swimming in it. How much water does it need per meter to fill up the pool?**

19 liters per meter [(129 ÷ 17) x 7=19].

**Georgina wants to bake a batch of muffins using 129 grams of sugar, but only knows recipes that call for 11 grams at a time. How many muffins will she be able to make from this amount of sugar?**

12 muffins (129 ÷ 11=12)

**If someone buys 130 apples for $10,2 cents more than each apple costs, what was the cost for one apple?**

9 cents (10÷130=0.09 ).

**A family reunion consists of 13 people so every family brings 11 food items. How many food items do they bring altogether?**

143 food items (13×11=143 )

**Jane buys 135 pencils each costing 6 cents less than each pen she purchases which costs 15 cents What is the total cost for all pencils?**

$9(135x 0 .06=$8 .1 +15=$9 )

Written by

Prerit Jain