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 = 2^{6}
 Sum of Factors of 64: 127
1.  What Are the Factors of 64? 
2.  How to Calculate Factors of 64? 
3.  Factors of 64 by Prime Factorization 
4.  Factors of 64 in Pairs 
5.  FAQs on Factors of 64 
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?
Two steps help us 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:
Factors  Pair Factors 
1× 64 = 64  (1, 64) 
2× 32 = 64  (2, 32) 
4 × 16 = 64  (4, 16) 
8 × 8 = 64  (8, 8) 
 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:
Factors  Pair Factors 
1 × 64 = 64  (1, 64) 
 2× 32 = 64  (2, 32) 
4× 16 = 64  (4, 16) 
8 ×  8 = 64  (8, 8) 
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.
Factors of 64 Solved Examples

Example 1: Jessy loves to draw different cartoons. She draws 2 cartoons every day. In how many days will she draw 64 cartoons?
Solution:
Total number of cartoons she has to draw = 64
To find the number of days she will take to draws 64 cartoons, we will divide 64 by 2
64 ÷ 2=32
We can also solve the problem by using the information that (2, 32) are pair factors of 64. So, having known that 2 as one of the 64, the other factor is 32
Hence, in 32 days she will draw 64 cartoons. 
Example 2: Help John find the negative pairs factors of 64
Solution:
Negative pair factors of 64 are given as:
Factors Pair Factors 1× 64 = 64 (1, 64)  2× 32 = 64 (2, 32) 4× 16 = 64 (4, 16) 8 ×  8 = 64 (8, 8) 
Example 3: A carrom board has an area of 64 square inches and a length of 8 inches. Determine its breadth.
Solution:
The area of the rectangle is length × breadth.
The length of the carrom board, which is 8 inches is a factor of the area, which is 64 inches²
When 8 is multiplied by 8, the product is 64
8 × 8 = 64
This shows that 8 is the factor of 64
Therefore, the breadth of the carrom board is 8 inches.
FAQs on Factors of 64
What are the Factors of 64?
The factors of 64 are 1, 2, 4, 8, 16, 32, 64 and its negative factors are 1, 2, 4, 8, 16, 32, 64.
What is the Sum of all the Factors of 64?
Sum of all factors of 64 = (2^{6 + 1}  1)/(2  1) = 127
What are the Common Factors of 64 and 57?
Since, the factors of 64 are 1, 2, 4, 8, 16, 32, 64, and factors of 57 are 1, 3, 19, 57. Hence, 64 and 57 have only one common factor which is 1. Therefore, 64 and 57 are coprime.
What numbers are the Pair Factors of 64?
The pair factors of 64 are (1, 64), (2, 32), (4, 16), (8, 8).
What is the Greatest Common Factor of 64 and 40?
The factors of 64 and 40 are 1, 2, 4, 8, 16, 32, 64 and 1, 2, 4, 5, 8, 10, 20, 40 respectively.
Common factors of 64 and 40 are [1, 2, 4, 8].
Hence, the Greatest Common Factor (GCF) of 64 and 40 is 8.
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