1. Steps to find factors of 1000 using Division Method

Example: Find factors of 1000

  • Divide 1000 by 1: 1000 ÷ 1 : Remainder = 0
  • Divide 1000 by 2: 1000 ÷ 2 : Remainder = 0
  • Divide 1000 by 4: 1000 ÷ 4 : Remainder = 0
  • Divide 1000 by 5: 1000 ÷ 5 : Remainder = 0
  • Divide 1000 by 8: 1000 ÷ 8 : Remainder = 0
  • Divide 1000 by 10: 1000 ÷ 10 : Remainder = 0
  • Divide 1000 by 20: 1000 ÷ 20 : Remainder = 0
  • Divide 1000 by 25: 1000 ÷ 25 : Remainder = 0
  • Divide 1000 by 40: 1000 ÷ 40 : Remainder = 0
  • Divide 1000 by 50: 1000 ÷ 50 : Remainder = 0
  • Divide 1000 by 100: 1000 ÷ 100 : Remainder = 0
  • Divide 1000 by 125: 1000 ÷ 125 : Remainder = 0
  • Divide 1000 by 200: 1000 ÷ 200 : Remainder = 0
  • Divide 1000 by 250: 1000 ÷ 250 : Remainder = 0
  • Divide 1000 by 500: 1000 ÷ 500 : Remainder = 0
  • Divide 1000 by 1000: 1000 ÷ 1000 : Remainder = 0

Hence, Factors of 1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, and 1000

2. Steps to find factors of 1000 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 1000 using the division method, follow these steps:

  • Step 1. Start dividing 1000 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 1000, which is 2. Divide 1000 by 2 to obtain the quotient (500).
    1000 ÷ 2 = 500
  • Step 3. Repeat step 1 with the obtained quotient (500).
    500 ÷ 2 = 250
    250 ÷ 2 = 125
    125 ÷ 5 = 25
    25 ÷ 5 = 5
    5 ÷ 5 = 1

So, the prime factorization of 1000 is, 1000 = 2 x 2 x 2 x 5 x 5 x 5.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1000 as shown below:

So, the prime factorization of 1000 is, 1000 = 2 x 2 x 2 x 5 x 5 x 5.

3. Find factors of 1000 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 1000 would be the two numbers which, when multiplied, give 1000 as the result.

The following table represents the calculation of factors of 1000 in pairs:

Factor Pair Pair Factorization
1 and 1000 1 x 1000 = 1000
2 and 500 2 x 500 = 1000
4 and 250 4 x 250 = 1000
5 and 200 5 x 200 = 1000
8 and 125 8 x 125 = 1000
10 and 100 10 x 100 = 1000
20 and 50 20 x 50 = 1000
25 and 40 25 x 40 = 1000

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 1000. They are called negative pair factors.

Hence, the negative pairs of 1000 would be ( -1 , -1000 ) , ( -2 , -500 ) , ( -4 , -250 ) , ( -5 , -200 ) , ( -8 , -125 ) , ( -10 , -100 ) , ( -20 , -50 ) and ( -25 , -40 ) .

What are factors?

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

Properties of factors

  • Each number is a factor of itself. Eg. 1000 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 1000.
  • Every number is a factor of zero (0), since 1000 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, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000 are exact divisors of 1000.
  • Factors of 1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000. Each factor divides 1000 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000 are all less than or equal to 1000.

Frequently Asked Questions

  • What are the prime factors of 1000?

    The factors of 1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000.
    Prime factors of 1000 are 2, 2, 2, 5, 5, 5.

  • What is the sum of all factors of 1000?

    The sum of all factors of 1000 is 2340.

  • What are the pair factors of 1000?

    Pair factors of 1000 are (1,1000), (2,500), (4,250), (5,200), (8,125), (10,100), (20,50), (25,40).

  • What two numbers make 1000?

    Two numbers that make 1000 are 2 and 500.

  • What are multiples of 1000?

    First five multiples of 1000 are 2000, 3000, 4000, 5000.

  • Is 1000 a perfect square?

    No 1000 is not a perfect square.

  • Which is greatest factor of 1000?

    The greatest factor of 1000 is 500.

  • How do you factors of 1000?

    Factors of 1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000.

  • What are five multiples of 1000?

    First five multiples of 1000 are 2000, 3000, 4000, 5000, 6000.

Examples of Factors

Can you help Rubel to find out the product of the even factors of 1000?

Factors of 1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000.
Even factors of 1000 are 2, 4, 8, 10, 20, 40, 50, 100, 200, 250, 500, 1000.
Hence, product of even factors of 1000 is; 2 x 4 x 8 x 10 x 20 x 40 x 50 x 100 x 200 x 250 x 500 x 1000 = 64000000000000000000.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 1000? Help her in writing all the factors.

Positive factors are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000.
Negative factors are -1, -2, -4, -5, -8, -10, -20, -25, -40, -50, -100, -125, -200, -250, -500, -1000.

How many factors are there for 1000?

Factors of 1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000.
So there are in total 16 factors.

Sammy is puzzled while calculating the prime factors of 1000. Can you help him find them?

Factors of 1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000.
Prime factors of 1000 are 2, 2, 2, 5, 5, 5

Joey wants to write all the prime factors of 1000 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1000 are 2, 2, 2, 5, 5, 5.
So in exponential form it can be written as 23 x 53.

What is prime factorization of 1000?

Prime factorization of 1000 is 2 x 2 x 2 x 5 x 5 x 5 = 23 x 53.

Can you help Rubel to find out the product of the even factors of 1000?

Factors of 1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000.
Even factors of 1000 are 2, 4, 8, 10, 20, 40, 50, 100, 200, 250, 500, 1000.
Hence, product of even factors of 1000 is; 2 x 4 x 8 x 10 x 20 x 40 x 50 x 100 x 200 x 250 x 500 x 1000 = 64000000000000000000.