Factors of 512
By the definition of a factor, a factor is always less than or equal to the given number. But to find the factors of a number, we don't need to check with all the numbers that are less than or equal to the given number. We can just check with the numbers from 1 to "half of the number." This is because any number that is more than half of the given number cannot be a factor of the given number. While dividing, if we get 0 at any point, then both the divisor and quotient of that division are the factors.
For example, when you divide 512 by 64, the remainder is 0. Let us find the factors of 512 using the above procedure. Factors of 512 are those numbers which when multiply together gives 512 as a result.
 Factors of 512 : 1, 2, 4, 8, 16, 32, 64, 128, 256, and 512.
 Prime Factorization of 512: 512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2^{9}
1.  What Are the Factors of 512? 
2.  How to Calculate Factors of 512? 
3.  Factors of 512 by Prime Factorization 
4.  Tips and Tricks 
5.  Factors of 512 in Pairs 
6.  Think Tank 
7.  FAQs on Factors of 512 
What are the Factors of 512?
The numbers that give a remainder of 0 when we divide 512 by them are called the factors of 512. For example, when 512 is divided by 64, the remainder is 0.
Hence, 64 is a factor of 512.
How to Calculate the Factors of 512?
Half of 512 is 256. So we will divide 512 by the numbers from 1 to 256, leaving the quotients of the division that give 0 as the remainder. Then we will get 0 as the remainder only in the following divisions.
 512 ÷ 2 = 256
 512 ÷ 4 = 128
 512 ÷ 8 = 64
 512 ÷ 16 = 32
Hence, the factors of 512 are, 1, 2, 4, 8, 16, 32, 64, 128, 256, and 512.
Explore factors using illustrations and interactive examples
 Factors of 125  The factors of 125 are 1, 5, 25, and 125.
 Factors of 256  The factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128 and 256.
 Factors of 216  The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216.
 Factors of 75  The factors of 75 are 1, 3, 5, 15, 25 and 75.
Factors of 512 by Prime Factorization
The prime factorization of 512 is expressing 512 as the product of prime numbers which result in 512.
 So the prime factorization of 512 is, 512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
 Hence, 512 = 2^{9}
 From the prime factorization of 512, it is clear that 2 is a factor of 512.
 2 is a prime factor of 512.
 By multiplying different sets of multiplicands of the above prime factorization, we can find the composite factors as well.
Tips and Tricks:
 When you divide a number by its factor, the quotient of the division is also a factor.
 A prime number has exactly two factors, 1 and the number itself.
 We can apply divisibility rules to find factors.
Factors of 512 in Pairs
The pair factors of 512 are obtained by writing 512 as a product of two numbers in all possible ways. In each product, both multiplicands are the factors of 512.
Product That Result in 512 
Pair Factors of 512 

1 × 512 
(1, 512) 
2 × 256 
(2, 256) 
4 × 128 
(4, 128) 
8 × 64 
(8, 64) 
16 × 32 
(16, 32) 
The negative pair factors of 512 are (1, 512), (2, 256), (4, 128), (8, 64), and (16, 32)
Thnk Tank:
 We know that 512, when divided by 0.4, leaves the remainder as 0. Does this mean that 0.4 is a factor of 512?
 We know that 512 ÷ 2/3 = 768. It means 512, when divided by 2/3, leaves the remainder as 0. Does this mean that 2/3 is a factor of 512?
Factors of 512 Solved Examples

Example 1: There are 512 monkeys in a zoo. Zookeeper William wants to group them in different cages as monkeys cause a lot of mischief if they are all together. He wants an equal number of monkeys in all the cages for easy maintenance. Also, he wants more than 10 and less than 60 monkeys in a cage. In how many ways he can do this?
Solution:
We already learned that the factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, and 512. Among these, the factors that are more than 10 and less than 60 are 16 and 32 (2 factors).
Thus, the required number of ways = 2 
Example 2: Benjamin needs to ship 74 rock music CDs and 512 pop music CDs by packing them in boxes. He is allowed to pack only one type of CD in each box. Also, he must pack the same number of CDs in each box. What is the number of CDs Benjamin can pack in each box?
Solution:
The factors of 74 are 1, 2, 37, and 74.
The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, and 512.
The common factors of 512 and 74 are 1 and 2
Thus, Benjamin can pack either 1 or 2 CDs in a box.
FAQs on Factors of 512
What are the prime factors of 512?
Prime factors of 512 are: 1 and 2
What are the positive pair factors of 512?
The psoitive pair factors of 512 are (1, 512), (2, 256), (4, 128), (8, 64), and (16, 32)
What are the negative pair factors of 512?
The negative pair factors of 512 are (1, 512), (2, 256), (4, 128), (8, 64), and (16, 32)
What is the prime factorization of 512?
The prime factorization of 512 is, 512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2^{9}
How many factors of 512 are there?
The factors of 512 are:1, 2, 4, 8, 16, 32, 64, 128, 256, and 512.
There are total 10 factors of 512.
visual curriculum