1. Steps to find factors of 1024 using Division Method

Example: Find factors of 1024

  • Divide 1024 by 1: 1024 ÷ 1 : Remainder = 0
  • Divide 1024 by 2: 1024 ÷ 2 : Remainder = 0
  • Divide 1024 by 4: 1024 ÷ 4 : Remainder = 0
  • Divide 1024 by 8: 1024 ÷ 8 : Remainder = 0
  • Divide 1024 by 16: 1024 ÷ 16 : Remainder = 0
  • Divide 1024 by 32: 1024 ÷ 32 : Remainder = 0
  • Divide 1024 by 64: 1024 ÷ 64 : Remainder = 0
  • Divide 1024 by 128: 1024 ÷ 128 : Remainder = 0
  • Divide 1024 by 256: 1024 ÷ 256 : Remainder = 0
  • Divide 1024 by 512: 1024 ÷ 512 : Remainder = 0
  • Divide 1024 by 1024: 1024 ÷ 1024 : Remainder = 0

Hence, Factors of 1024 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, and 1024

2. Steps to find factors of 1024 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

Method 1: Division Method

To find the primefactors of 1024 using the division method, follow these steps:

  • Step 1. Start dividing 1024 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
  • Step 2. After finding the smallest prime factor of the number 1024, which is 2. Divide 1024 by 2 to obtain the quotient (512).
    1024 ÷ 2 = 512
  • Step 3. Repeat step 1 with the obtained quotient (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

So, the prime factorization of 1024 is, 1024 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1024 as shown below:

So, the prime factorization of 1024 is, 1024 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2.

3. Find factors of 1024 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 1024 would be the two numbers which, when multiplied, give 1024 as the result.

The following table represents the calculation of factors of 1024 in pairs:

Factor Pair Pair Factorization
1 and 1024 1 x 1024 = 1024
2 and 512 2 x 512 = 1024
4 and 256 4 x 256 = 1024
8 and 128 8 x 128 = 1024
16 and 64 16 x 64 = 1024
32 and 32 32 x 32 = 1024

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 1024. They are called negative pair factors.

Hence, the negative pairs of 1024 would be ( -1 , -1024 ) , ( -2 , -512 ) , ( -4 , -256 ) , ( -8 , -128 ) , ( -16 , -64 ) and ( -32 , -32 ) .

How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

Properties of factors

  • Each number is a factor of itself. Eg. 1024 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 1024.
  • Every number is a factor of zero (0), since 1024 x 0 = 0.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Every factor of a number is an exact divisor of that number, example 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 are exact divisors of 1024.
  • Factors of 1024 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024. Each factor divides 1024 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 are all less than or equal to 1024.

Frequently Asked Questions

  • Which is the smallest prime factor of 1024?

    The smallest prime factor of 1024 is 2.

  • Is 1024 a whole number?

    Yes 1024 is a whole number.

  • What are the prime factors of 1024?

    The factors of 1024 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024.
    Prime factors of 1024 are 2, 2, 2, 2, 2, 2, 2, 2, 2, 2.

  • What two numbers make 1024?

    Two numbers that make 1024 are 2 and 512.

  • What are multiples of 1024?

    First five multiples of 1024 are 2048, 3072, 4096, 5120.

  • What is the sum of all factors of 1024?

    The sum of all factors of 1024 is 2047.

  • What are five multiples of 1024?

    First five multiples of 1024 are 2048, 3072, 4096, 5120, 6144.

  • Is 1024 a perfect square?

    Yes 1024 is a perfect square.

  • What is the greatest prime factors of 1024?

    The greatest prime factor of 1024 is 2.

Examples of Factors

How many factors are there for 1024?

Factors of 1024 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024.
So there are in total 11 factors.

Kevin has been asked to write 10 factor(s) of 1024. Can you predict the answer?

10 factor(s) of 1024 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512.

Sammy is puzzled while calculating the prime factors of 1024. Can you help him find them?

Factors of 1024 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024.
Prime factors of 1024 are 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

What is prime factorization of 1024?

Prime factorization of 1024 is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 210.

Ariel has been assigned the task to find the product of all the prime factors of 1024. Can you help her?

Prime factors of 1024 are 2, 2, 2, 2, 2, 2, 2, 2, 2, 2.
Hence, the product of prime factors of 2.

Can you help Rubel to find out the product of the even factors of 1024?

Factors of 1024 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024.
Even factors of 1024 are 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024.
Hence, product of even factors of 1024 is; 2 x 4 x 8 x 16 x 32 x 64 x 128 x 256 x 512 x 1024 = 36028797018963970.

Joy wants to calculate mean of all the factors of 1024. Help him in finding the mean of 1024.

Factors of 1024 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 1024 is 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1024 = 2047.
Hence, the mean of factors of 1024 is 2047 ÷ 11 = 186.09.