Factors of 64

Factors of 64 are the list of integers that can be evenly divided into 64. There are overall 7 factors of 64 i.e. 1, 2, 4, 8, 16, 32, and 64 where 64 is the biggest factor. The Prime Factors of 64 are 1, 2, 4, 8, 16, 32, 64 and its Factors in Pairs are (1, 64), (2, 32), (4, 16), and (8, 8).

• Factors of 64: 1, 2, 4, 8, 16, 32 and 64
• Negative Factors of 64: -1, -2, -4, -8, -16, -32 and -64
• Prime Factors of 64: 2
• Prime Factorization of 64: 2 × 2 × 2 × 2 × 2 × 2 = 2⁶
• Sum of Factors of 64: 127

What are the Factors of 64?

Let us recall the meaning of the term 'factor'.

• A factor is a number that divides into another number completely without leaving any remainder.
• Factors of 64 are the numbers which when multiplied together result in 44
• 2 and 32 are the factors of 64.

Let us see how to calculate the factors of 64

How to Calculate the Factors of 64?

• Step 1: Write down the number to be factored, that is, 64
• Step 2: Find the two numbers whose product is 64

Let's say we take 2 and 32 to be the two factors. 2 is a prime number, therefore, it cannot further be split. 32 is not a prime number. Hence, it can be factorized as a product of 4 and 8, apart from the product of 1 and the number itself. 32 can be written as: 4 × 8 = 32. 64 can be written as: 64 =  2 × 4 × 8 or 2 × 2 × 2 × 2 × 2 × 2 

Hence, the factors of 64 are 1, 2, 4, 8, 16, 32, and 64.

Explore factors using illustrations and interactive examples.

• Factors of 144 - The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
• Factors of 44 - The factors of 44 are 1, 2, 4, 11, 22, and 44
• Factors of 32 - The factors of 32 are 1, 2, 4, 8, 16, and 32
• Factors of 40 - The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40 1 , 2 , 4 , 5 , 8 , 10 , 20 , 40 
• Factors of 34: The factors of 34 are 1, 2, 17, and 34
• Factors of 45 - The factors of 45 are 1, 3, 5, 9, 15, 45

Factors of 64 by Prime Factorization

Prime factorization is the process of writing a number as a product of its prime factors. Let us learn how to find the factors of a number using prime factorization.

• Step 1: Write the pair of factors, which on multiplication give the required number.
• Step 2: Check whether the factors are prime or not.
• If both the numbers are prime, they can be multiplied as it is. 
• If one of them is prime and the other one is composite, then the composite number is further split into its factors.
• If both the numbers are composite, they can be further split into their factors.

Let us find the factors of 64 by prime factorization using these steps.

• Step 1: 64 can be factored as a product of 2 and 32
• Step 2: 32 is not a prime number and can further be factored as a product of 4 by 8.
• Step 3: Therefore, 64 can be written as:

64 = 2 × 32 =  2 × 2 × 2 × 2 × 2 × 2 

It can also be written as 64 = 2^6. Observe this factor tree.

Important Notes:

• Factors of any number are all the possible numbers that can divide the number without leaving any remainder.
  They may be prime numbers or composite numbers.
• Factors can never be fractions or decimals.
• Factors can be negative.

Factors of 64 in Pairs

Factors are often written as pairs of numbers, which when multiplied together give the original number. Here, the required number is 64. 64 can have the following pair factors:

• The factors given above are the positive pair factors of 64
• It is possible to have negative pair factors as well because the product of two negative numbers also gives a positive number.
• Let's have a look at the negative pair factors of 64:

Challenging Questions:

• Why is 64 not a triangular number?
• Is 64 a perfect square number? Why?

Tips and Tricks:

• 1 is the smallest factor of every number.
• Every number has a minimum of 2 factors, that is, 1 and the number itself.
• All even numbers always have 2 as one of their factors. For example factors of 64 are 1, 2, 4, 8, 16, 32, and 64.