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Factors of 1024

Factors of 1024 are the list of integers that we can split evenly into 1024. There are 11 factors of 1024, of which the following are its prime factors 2. The sum of all factors of 1024 is 2047.

  • All Factors of 1024: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512 and 1024
  • Prime Factors of 1024: 2
  • Prime Factorization of 1024: 210
  • Sum of Factors of 1024: 2047
1. What Are the Factors of 1024?
2. Factors of 1024 by Prime Factorization
3. Factors of 1024 in Pairs
4. FAQs on Factors of 1024
Factors of 1024

What are Factors of 1024?

Factors of 1024 are pairs of those numbers whose products result in 1024. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1024?

To find the factors of 1024, we will have to find the list of numbers that would divide 1024 without leaving any remainder.

  • 1024/256 = 4; therefore, 256 is a factor of 1024 and 4 is also a factor of 1024.
  • 1024/512 = 2; therefore, 512 is a factor of 1024 and 2 is also a factor of 1024.
Similarly we can find other factors. Hence, the factors of 1024 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024.

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Factors of 1024 by Prime Factorization

The number 1024 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1024. The first step is to divide the number 1024 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 1024 ÷ 2 = 512
  • 512 ÷ 2 = 256
  • 256 ÷ 2 = 128
  • 128 ÷ 2 = 64
  • 64 ÷ 2 = 32
  • 32 ÷ 2 = 16
  • 16 ÷ 2 = 8
  • 8 ÷ 2 = 4
  • 4 ÷ 2 = 2
  • 2 ÷ 2 = 1

Further dividing 1 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 1 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.

Since, we can't divide any further in this case so we stop.

So, the prime factorization of 1024 is 210.

 

Factors of 1024 in Pairs

Pair factors of 1024 are the pairs of numbers that when multiplied give the product 1024. The factors of 1024 in pairs are:

  • 1 × 1024 = (1, 1024)
  • 2 × 512 = (2, 512)
  • 4 × 256 = (4, 256)
  • 8 × 128 = (8, 128)
  • 16 × 64 = (16, 64)
  • 32 × 32 = (32, 32)

Negative pair factors of 1024 are:

  • -1 × -1024 = (-1, -1024)
  • -2 × -512 = (-2, -512)
  • -4 × -256 = (-4, -256)
  • -8 × -128 = (-8, -128)
  • -16 × -64 = (-16, -64)
  • -32 × -32 = (-32, -32)

NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.

Factors of 1024 Solved Examples

  1. Example 1: How many factors are there for 1024?

    Solution:

    The factors of 1024 are too many, therefore if we can find the prime factorization of 1024, then the total number of factors can be calculated using the formula shown below.
    If the prime factorization of the number is ax × by × cz where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1).

    Prime Factorization of 1024 = 210
    Therefore, the total number of factors are (10 + 1) = 11

  2. Example 2: Find the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of 1024 and 531.

    Solution:

    The factors of 1024 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 and factors of 531 are 1, 3, 9, 59, 177, 531.

    Therefore, the Least Common Multiple (LCM) of 1024 and 531 is 543744 and Greatest Common Divisor (GCD) of 1024 and 531 is 1.

  3. Example 3: Find if 2, 8, 128, 256, 891 and 1024 are factors of 1024.

    Solution:

    When we divide 1024 by 891 it leaves a remainder. Therefore, the number 891 is not a factor of 1024. All numbers except 891 are factors of 1024.

  4. Example 4: Find the product of all the prime factors of 1024.

    Solution:

    Since, the prime factor of 1024 is 2. Therefore, the product of prime factors = 2.

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FAQs on Factors of 1024

What are the Factors of 1024?

The factors of 1024 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 and its negative factors are -1, -2, -4, -8, -16, -32, -64, -128, -256, -512, -1024.

What is the Sum of all Factors of 1024?

Sum of all factors of 1024 = (210 + 1 - 1)/(2 - 1) = 2047

What are Prime Factors of 1024?

The prime factor of 1024 is 2.

What is the Greatest Common Factor of 1024 and 106?

The factors of 1024 and 106 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 and 1, 2, 53, 106 respectively.

Common factors of 1024 and 106 are [1, 2].

Hence, the GCF of 1024 and 106 is 2.

How Many Factors of 1024 are also Factors of 897?

Since, the factors of 1024 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 and factors of 897 are 1, 3, 13, 23, 39, 69, 299, 897. Hence, 1024 and 897 have only one common factor which is 1. Therefore, 1024 and 897 are co-prime.

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