Factors

# Factors of 69 | Prime Factorization of 69 | Factor Tree of 69

Written by Prerit Jain

Updated on: 09 Jun 2023

Contents

### Factors of 69 | Prime Factorization of 69 | Factor Tree of 69

## Factors of 69

Factors of 69 | Factor Pairs of 69 | Prime factors of 69 |

1, 3, 23, and 69 | (1, 69) and (3, 23) | 3 x 23 |

**Factors of 69**,

**Factor Pairs of 69**,

**Prime factors of 69**

Calculate Factors of

**The Factors are**

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## What are the factors of 69

The factors of 69 can be found through the following method:

- Write down the number you want to find the factors of.
- Write down the number 1. This is always a factor of any number.
- Write down the number itself. This is also always a factor of any number.
- Divide the number by 2. If the division is even, write down the result as a factor. If the division is not even, skip this step.
- Starting from 3, count up in increments of 1 and divide the number by each increment. If the division is even, write down the result as a factor.
- Repeat this process until you have tried all the possible factors.

For example, let’s find the factors of 69 using this method. First, we write down 1 and 69 as factors. Then, we divide 69 by 2 and get a result of 34.5, which is not an even division, so we skip this step. Next, we start counting up from 3 and dividing 69 by each increment. When we divide 69 by 3, we get a result of 23, which is an even division, so we write down 23 as a factor. We continue counting up and dividing until we reach 69, at which point we stop because we have already tried all the possible factors.

**So the factors of 69 are 1, 3, 23, and 69. **

## How to Find Factors of 69

Here are a few steps you can follow to find the factors of 69:

- Factors of 69 using the Multiplication Method
- Factors of 69 using the Division Method
- Prime Factorization of 69
- Factor tree of 69

## Factors of 69 Using the Multiplication Method

- Write down the number you want to find the factors of.
- Determine which whole numbers, starting from 2, can be multiplied by 1 to produce the number you are trying to factor. These numbers will be the factors of the original number.
- Start by multiplying 1 by 2, then 3, 4, and so on, up to the square root of the number you are trying to factor.
- If the result of any of these multiplications is equal to the number you are trying to factor, write down the number you multiplied by 1 as a factor.
- For each factor you found in Step 4, divide the number you are trying to factor by that factor. If the division is even, write down the result as a factor.
- Repeat this process until you have tried all the possible factors.

Using this method, you can find all the factors of a number by multiplying 1 by different whole numbers and checking if the result is equal to the number you are trying to factor.

For example, to find the factors of 69, you would start by multiplying 1 by 2, then 3, 4, and so on, up to the square root of 69, which is 8.3. You would find that 23 and 3 are both factors of 69 because 69 divided by 23 and 69 divided by 3 are both even divisions.

**So the factors of 69 are 1, 3, 23, and 69.**

## Factors of 69 Using the Division Method

- Write down the number you want to find the factors of.
- Write down the number 1. This is always a factor of any number.
- Write down the number itself. This is also always a factor of any number.
- Starting from 2, count up in increments of 1 and divide the number you are trying to factor by each increment.
- If the division is even, write down the result as a factor.
- Repeat this process until you have tried all the possible factors.

Using this method, you can find the factors of a number by dividing it by different whole numbers and checking if the division is even.

For example, to find the factors of 69, you would start by dividing 69 by 2 and get a result of 35, which is not an even division. You would then continue counting up from 3 and dividing 69 by each increment until you reach 69, at which point you would stop because you have already tried all the possible factors. You would find that 23 and 3 are both factors of 69 because 69 divided by 23 and 69 divided by 3 are both even divisions.

**So the factors of 69 are 1, 3, 23, and 69.**

## Prime Factorization of 69

Calculate Prime Factors of

The Prime Factors of 69 =

3 x

23

The prime factorization of 69 is the expression of 69 as the product of its prime factors. The prime factorization of 69 is 3 x 23 because 69 can be expressed as the product of the prime numbers 3 and 23 (3 x 23 = 69).

To find the prime factorization of a number, you can express the number as the product of its prime factors. For example, the prime factorization of 24 is 2 x 2 x 2 x 3, because 24 can be expressed as the product of the prime numbers 2, 2, 2, and 3 (2 x 2 x 2 x 3 = 24).

The prime factorization of a number is written as the product of its prime factors. **For example, the prime factorization of 69 is written as 3 x 23.**

## Factor tree of 69

- Write the number you want to find the prime factorization of at the top of the tree.
- Divide the number by the smallest possible prime factor (usually 2). Write the result of the division and the factor you divided by on separate branches of the tree.
- Repeat this process for each branch of the tree until you can’t divide any of the numbers by any more prime factors. The numbers on the final branches of the tree will be the prime factors of the original number.

A factor tree is a visual representation of the prime factorization of a number. It shows how a number can be written as the product of its prime factors. To create a factor tree, you divide a number by its smallest possible prime factor and write the result and the factor you divided by on separate branches of the tree. You then repeat this process for each branch until you reach the prime factors of the original number.

For example, to create a factor tree for 69, you would first divide 69 by the smallest possible prime factor, which is 2. Since the division is not even, you would move on to the next smallest prime factor, which is 3. You would divide 69 by 3 and get a result of 23. You couldn’t divide 23 by any more prime factors, so the prime factorization of 69 is 3 x 23.

## Factor Pairs of 69

Calculate Pair Factors of

1 x 69=69

3 x 23=69

23 x 3=69

So Pair Factors of 69 are

(1,69)

(3,23)

(23,3)

- Write down the number you want to find the factor pairs of.
- Write down the number 1. This is always a factor of any number.
- Write down the number itself. This is also always a factor of any number.
- Starting from 2, count up in increments of 1 and divide the number you are trying to find the factor pairs of by each increment.
- If the division is even, write down the result as a factor and pair it with the number you divided by.
- Repeat this process until you have tried all the possible factors.

The factor pairs of a number are all the pairs of numbers that can be multiplied together to equal that number. To find the factor pairs of a number, you can divide the number by different whole numbers and pair the result with the number you divided by if the division is even.

For example, to find the factor pairs of 69, you would start by dividing 69 by 2 and get a result of 35, which is not an even division, so you would skip this step. You would then continue the same for other numbers.

## More Factors

- Factors of 66
- Factors of 67
- Factors of 68
- Factors of 69
- Factors of 70
- Factors of 71
- Factors of 72

## Factors of 69 – Quick Recap

**Factors of 69:** 1, 3, 23, and 69

**Negative Factors of 69:** -1, -3, -23, and -69.

**Prime Factors of 69:** 3 x 23

**Prime Factorization of 69:** 3 x 23

## Factors of 69 – Fun Facts

- 69 is a composite number, which means it is a positive integer that has more than two factors. The factors of 69 are 1, 3, 23, and 69.
- 69 is an odd number, which means it is not divisible by 2.
- The prime factorization of 69 is 3 x 23, which means that it can be written as the product of two prime numbers (3 and 23).
- The sum of the factors of 69 is 96, which is 27 more than the number itself (69).
- The product of the factors of 69 is 1617, which is 23 times more than the number itself (69).

**Also Check**: Multiples, Square Root, and LCM

## Examples of Factor of 69

**Q.1: What pairs of numbers multiplied together would equal sixty-nine? ****Solution:** Two numbers which when multiplied together would equal sixty-nine are 1×69 and 3×23; 1×69=69 & 3×23= 67.

**Q.2:** If you divide sixty-nine by three, what will the remainder be? **Solution: **The remainder when dividing sixty-nine by three is zero; 69/3= 23 with a remainder of 0.

**Q.3:** How many even numbers remain between one and sixty-nine when all odd numbers are removed? **Solution: **Thirty-four even numbers remain between one and sixty-nine when all odd numbers are removed; these would include 2, 4, 6, 8 10, 12 14, 16 18, 20 22, 24 26, 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 & 68.

**Q.4:** Find the prime factorization of sixty-nine? **Solution: **The prime factorization of sixty-nine is 69 = 3 x 23; both being prime numbers.

**Q.5:** Paul needs to multiply three unequal numbers together in order to generate a total of eighty-eight, which combination can he use? **Solution:**Number combinations that can be used to multiply together to total eighty-eight are 2x4x11 = 88.

**Q.6:** Find the greatest common factor for twenty-seven and thirty-one? **Solution: **The greatest common factor for twenty-seven and thirty-one is one as neither can be divided evenly without a remainder over another number apart from themselves or one (27/31= 0.8709677).

**Q.7:** What pair of prime numbers can only be divided evenly with themselves and one in order to produce a total that equals fifty-five? **Solution:** Two prime numbers that can only be divided evenly with themselves and one in order to produce a total that equals fifty-five are 55 & 1; 55 x1=55and neither can be divided evenly with another number apart from themselves or one in order to equal fifty-five.

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## Frequently Asked Questions on Factors of 69

**What pairs of numbers multiplied together would equal sixty-nine?**

Two numbers which when multiplied together would equal sixty-nine are 1×69 and 3×23; 1×69=69 & 3×23= 69.

**If you divide sixty-nine by three, what will the remainder be?**

The remainder when dividing sixty-nine by three is zero; 69/3= 23 with a remainder of 0.

**How many even numbers remain between one and sixty-nine when all odd numbers are removed?**

Thirty-four even numbers remain between one and sixty-nine when all odd numbers are removed; these would include 2, 4, 6, 8 10, 12 14, 16 18, 20 22, 24 26, 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 & 68.

**Find the prime factorization of sixty-nine.**

The prime factorization of sixty-nine is 69 = 3 x 23; both being prime numbers.

**Paul needs to multiply three unequal numbers together in order to generate a total of eighty-eight, which combination can he use?**

Number combinations that can be used to multiply together to total eighty-eight are 2x4x11 = 88.

**Find the greatest common factor for twenty-seven and thirty-one.**

The greatest common factor for twenty-seven and thirty-one is one as neither can be divided evenly without a remainder over another number apart from themselves or one (27/31=0.8709677).

**What pair of prime numbers can only be divided evenly with themselves and one in order to produce a total that equals fifty-five?**

Two prime numbers that can only be divided evenly with themselves and one in order to produce a total that equals fifty-five are 55 & 1; 55 x1=55 and neither can be divided evenly with another number apart from themselves or one in order to equal fifty-five.

Written by

Prerit Jain