Factors

# Factors of 64 | Prime Factorization of 64 | Factor Tree of 64

Written by Prerit Jain

Updated on: 09 Jun 2023

Contents

### Factors of 64 | Prime Factorization of 64 | Factor Tree of 64

## Factors of 64

Factors of 64 | Factor Pairs of 64 | Prime factors of 64 |

1, 2, 4, 8, 16, 32, 64 | (1,64) (2,32) (4,16) (8,8) (16,4) (32,2) | 2 x 2 x 2 x 2 x 2 x 2 |

**Factors of 64**,

**Factor Pairs of 64**,

**Prime factors of 64**

Calculate Factors of

**The Factors are**

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## What are the factors of 64

The factors of 64 are the numbers that can be multiplied together to equal 64. **The factors of 64 include 1, 2, 4, 8, 16, 32, and 64.** These numbers are all factors of 64 because they can all be multiplied together to get 64. For example, 1 x 64 = 64, 2 x 32 = 64, and so on.

You can find the factors of a number by dividing the number by each of the numbers from 1 to itself, and seeing which pairs result in a whole number. For example, to find the factors of 64, you would divide 64 by 1, 2, 3, etc. until you reach 64. The pairs that result in a whole number are the factors.

## How to Find Factors of 64

To find the factors of 64, you can use one of the following methods:

- Factors of 64 using the Multiplication Method
- Factors of 64 using the Division Method
- Prime Factorization of 64
- Factor tree of 64

## Factors of 64 Using the Multiplication Method

To find the factors of a number, you can divide the number by each of the numbers from 1 to itself and see which pairs result in a whole number. These pairs are the factors of the original number.

For example, to find the factors of 64 using the multiplication method:

- Start with the number 64.
- Divide 64 by 1. If the result is a whole number, then 1 is a factor of 64. In this case, the result is 64, which is a whole number, so 1 is a factor of 64.
- Divide 64 by 2. If the result is a whole number, then 2 is a factor of 64. In this case, the result is 32, which is a whole number, so 2 is a factor of 64. n this case, the result is 21.3.
- Divide 64 by the next smallest number, which is 3. If the result is a whole number, then 3 is a factor of 64. In this case, the result is 21.3.

## Factors of 64 Using the Division Method

To find the factors of a number using the division method, you can follow these steps:

- Start with the number you want to find the factors of.
- Divide the number by 2. If the result is a whole number, then 2 is a factor of the original number.
- Divide the number by the next smallest number, which is 3. If the result is a whole number, then 3 is a factor of the original number.
- Continue dividing the number by the next smallest number until you reach the original number. Any time the result is a whole number, the divisor is a factor of the original number.

For example, to find the factors of 64 using the division method:

- Start with the number 64.
- Divide 64 by 2. If the result is a whole number, then 2 is a factor of 64.
- Divide 64 by 3. If the result is a whole number, then 3 is a factor of 64.
- Continue dividing 64 by the next smallest number (4, 5, etc.) until you reach 64. Any time the result is a whole number, the divisor is a factor of 64.

Using this method, you can systematically find all the factors of a number without using specific numbers. You just need to keep dividing the number by the next smallest number until you reach the original number, and any time the result is a whole number, the divisor is a factor of the original number.

## Prime Factorization of 64

Calculate Prime Factors of

The Prime Factors of 64 =

2 x

2 x

2 x

2 x

2 x

2

The prime factorization of 64 is the expression of 64 as the product of its prime factors. The prime factorization of 64 is 2 x 2 x 2 x 2 x 2 x 2, because 64 can be expressed as the product of six 2s (2 x 2 x 2 x 2 x 2 x 2 = 64).

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 15 is 3 x 5, because 15 can be expressed as the product of the prime numbers 3 and 5 (3 x 5 = 15).

The prime factorization of a number is written as the product of its prime factors. For example, the prime factorization of 64 is written as 2 x 2 x 2 x 2 x 2 x 2.

## Factor tree of 64

To create a factor tree for a number using the division method, you can follow these steps:

- Start with the number you want to create a factor tree for.
- Divide the number by 2. If the result is a whole number, then 2 is a factor of the original number.
- Divide the number by the next smallest number (3). If the result is a whole number, then 3 is a factor of the original number.
- Continue dividing the number by the next smallest number until you reach a prime number.
- Repeat the process for each of the factors you found until all the factors are prime numbers.

Using this method, you can create a factor tree for any number without using specific numbers. You just need to keep dividing the number by the next smallest number until you reach a prime number, and then repeat the process for each of the factors you found until all the factors are prime numbers.

## Factor Pairs of 64

Calculate Pair Factors of

1 x 64=64

2 x 32=64

4 x 16=64

8 x 8=64

16 x 4=64

32 x 2=64

So Pair Factors of 64 are

(1,64)

(2,32)

(4,16)

(8,8)

(16,4)

(32,2)

A factor pair is a combination of two numbers that, when multiplied together, produce a specific target number. For example, the factor pair (2, 32) is one of the pairs that can be used to multiply and get 64 (2 * 32 = 64).

Factors are the numbers that can be divided into a target number without a remainder. For example, the factors of 64 include 1, 2, 4, 8, 16, 32, and 64. These numbers can all be divided into 64 without any remainder.

To find all of the factor pairs of a number, you can take the factors of that number and combine them in every possible way to create pairs. For example, the factor pairs of 64 include (1, 64), (2, 32), (4, 16), and (8, 8).

## More Factors

## Factors of 64 – Quick Recap

**Factors of 64:**1, 2, 4, 8, 16, 32, and 64.**Negative Factors of 64:**-1, -2, -4, -8, -16, -32, -64.**Prime Factors of 64:**2 x 2 × 2 x 2 x 2 x 2**Prime Factorization of 64:**2 x 2 x 2 x 2 x 2 x 2

## Factors of 64 – Fun Facts

- The factors of 64 are the numbers that can be multiplied together to produce 64. The factors of 64 are 1, 2, 4, and 64.
- The number 64 is a perfect cube, which means that it can be written as the product of three equal integers. In this case, the three equal integers are 2 x 2 x 2, or 2^3.
- The number 64 is also a perfect power of 2. This means that it can be written as the product of two equal integers, with one of the integers being 2. In this case, the two equal integers are 2 x 2, or 2^2.
- The number 64 is considered to be a lucky number in some cultures, as it is considered to be a symbol of abundance and prosperity.

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

## Solved Examples of Factor of 64

**Q.1: What is the Greatest Common Factor (GCF) of 64? ****Solution: **The greatest common factor (GCF) of 64 is 8, it’s the largest number which both can be divided without a remainder.

** Q.2:How many factors does sixty-four have?Solution:** Sixty-four has seven different factors; these include 1, 2, 4, 8 16, 32, and 64.

**Q.3:Is 15 a multiple or a factor of 64? Solution:** 15 is not a multiple or factor of sixty-four as it cannot be divided evenly with no remainder (15/64 = 0.234375).

** Q.4: Find three prime numbers whose product equals four hundred eighty-one when multiplied together. Solution:** Three prime numbers whose product equals four hundred eighty-one when multiplied together are 3, 3, and 53; 3x3x53= 481.

** Q.5:Patrick needs to divide an equation into equal parts however each part must be divisible by eight; what equation could he use? Solution: **Patrick could use 70×7=490 as this equation can be divided into two equal parts both divisible by eight (490/8 = 61 & 490/61 = 8).

**Thirty-one odd numbers remain between one and sixty-four when all even numbers are removed; these would include 1, 3, 5, 7, 9 11, 13, 15, 17 19, 21 23, 25 27 29, 31 33, 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 & 64.**

Solution:

**Q.6:**How many odd numbers remain between 1-64 when all even numbers are removed?Solution:

** Q.7: Find two prime numbers that can only be divided evenly by themselves and one to generate a product that totals sixteen. Solution:** Two prime numbers that can only be divided evenly by themselves and one to generate a product that totals sixteen are 16 & 1; 16×1=16and neither can be divided evenly with another number apart from themselves or one in order to equal sixteen.

** Q.8: If there are five unequal numbers multiplied together which is the greatest possible total if their product equals forty? Solution:** The greatest possible total if five unequal numbers multiplied together equal forty is 8; 2x2x2x5 x8=40.

** Q.9: How many pairs of factors are needed in order to multiply together in order to generate fifty-six? **Solution: Two pairs of factors need multiplying together in order to generate fifty-six; these would include 7×8=56 & 1 x56= 56.

**10. What two consecutive even numbers add up to sixty-eight while their product remains divisible by eight?**

**Solution:**Two consecutive even numbers adding up to sixty-eight while keeping their product divisible by eight are 32& 34 (32+34 = 68 & 32×34 =1088);1088/8 = 136.

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**What is the Greatest Common Factor (GCF) of 29?**

The greatest common factor (GCF) of 29 is 9, it’s the largest number which both can be divided without a remainder.

**How many factors does twenty-nine have?**

Twenty-nine has five different factors; these include 1, 29, and its prime numbers are 3 and 9.

**Is 18 a multiple or a factor of 29?**

18 is a multiple but not a factor of twenty-nine as it cannot be divided evenly with no remainder (18/29 = 0.6206896552).

**Find three prime numbers whose product equals eighty-nine when multiplied together.**

Three prime numbers whose product equals eighty-nine when multiplied together are 3, 3, and 31; 3x3x31= 89.

**Henry needs to divide an equation into equal parts however each part must be divisible by nine; what equation could he use?**

** **Henry could use 54×7=378 as this equation can be divided into two equal parts both divisible by nine (378/9 = 42 & 378/42 = 9).

**How many odd numbers remain between 1-29 when all even numbers are removed?**

Thirteen odd numbers remain between one and twenty-nine when all even numbers are removed; these would include 1, 3, 5, 7, 9 11, 13, 15 17, 19 21, 23 25, 27 & 29.

** Find two prime numbers that can only be divided evenly by themselves and one to generate a product that totals ninety-six.**

Two prime numbers that can only be divided evenly by themselves and one to generate a product that totals ninety-six are 96 & 1; 96×1=96and neither can be divided evenly with another number apart from themselves or one in order to equal ninety-six.

**If there are five unequal numbers multiplied together which is the greatest possible total if their product equals one hundred twenty?**

** **The greatest possible total if five unequal numbers multiplied together equal one hundred twenty is 24; 2x2x3x5 x24=120.

**How many pairs of factors are needed in order to multiply together in order to generate one hundred forty-seven?**

Two pairs of factors need multiplying together in order to generate one hundred forty-seven; these would include 7×7=49 & 3 x49= 147.

**What two consecutive odd numbers add up to thirty-four while their product remains divisible by nine?**

Two consecutive odd numbers adding up to thirty-four while keeping their product divisible by nine are 15& 17(15+17 = 34 & 15×17 =255);255/9 = 28.

Written by by

Prerit Jain