1. Steps to find factors of 2000 using Division Method

Example: Find factors of 2000

  • Divide 2000 by 1: 2000 ÷ 1 : Remainder = 0
  • Divide 2000 by 2: 2000 ÷ 2 : Remainder = 0
  • Divide 2000 by 4: 2000 ÷ 4 : Remainder = 0
  • Divide 2000 by 5: 2000 ÷ 5 : Remainder = 0
  • Divide 2000 by 8: 2000 ÷ 8 : Remainder = 0
  • Divide 2000 by 10: 2000 ÷ 10 : Remainder = 0
  • Divide 2000 by 16: 2000 ÷ 16 : Remainder = 0
  • Divide 2000 by 20: 2000 ÷ 20 : Remainder = 0
  • Divide 2000 by 25: 2000 ÷ 25 : Remainder = 0
  • Divide 2000 by 40: 2000 ÷ 40 : Remainder = 0
  • Divide 2000 by 50: 2000 ÷ 50 : Remainder = 0
  • Divide 2000 by 80: 2000 ÷ 80 : Remainder = 0
  • Divide 2000 by 100: 2000 ÷ 100 : Remainder = 0
  • Divide 2000 by 125: 2000 ÷ 125 : Remainder = 0
  • Divide 2000 by 200: 2000 ÷ 200 : Remainder = 0
  • Divide 2000 by 250: 2000 ÷ 250 : Remainder = 0
  • Divide 2000 by 400: 2000 ÷ 400 : Remainder = 0
  • Divide 2000 by 500: 2000 ÷ 500 : Remainder = 0
  • Divide 2000 by 1000: 2000 ÷ 1000 : Remainder = 0
  • Divide 2000 by 2000: 2000 ÷ 2000 : Remainder = 0

Hence, Factors of 2000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, and 2000

2. Steps to find factors of 2000 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 2000 using the division method, follow these steps:

  • Step 1. Start dividing 2000 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 2000, which is 2. Divide 2000 by 2 to obtain the quotient (1000).
    2000 ÷ 2 = 1000
  • Step 3. Repeat step 1 with the obtained quotient (1000).
    1000 ÷ 2 = 500
    500 ÷ 2 = 250
    250 ÷ 2 = 125
    125 ÷ 5 = 25
    25 ÷ 5 = 5
    5 ÷ 5 = 1

So, the prime factorization of 2000 is, 2000 = 2 x 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 2000 as shown below:

So, the prime factorization of 2000 is, 2000 = 2 x 2 x 2 x 2 x 5 x 5 x 5.

3. Find factors of 2000 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 2000 would be the two numbers which, when multiplied, give 2000 as the result.

The following table represents the calculation of factors of 2000 in pairs:

Factor Pair Pair Factorization
1 and 2000 1 x 2000 = 2000
2 and 1000 2 x 1000 = 2000
4 and 500 4 x 500 = 2000
5 and 400 5 x 400 = 2000
8 and 250 8 x 250 = 2000
10 and 200 10 x 200 = 2000
16 and 125 16 x 125 = 2000
20 and 100 20 x 100 = 2000
25 and 80 25 x 80 = 2000
40 and 50 40 x 50 = 2000

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 2000. They are called negative pair factors.

Hence, the negative pairs of 2000 would be ( -1 , -2000 ) , ( -2 , -1000 ) , ( -4 , -500 ) , ( -5 , -400 ) , ( -8 , -250 ) , ( -10 , -200 ) , ( -16 , -125 ) , ( -20 , -100 ) , ( -25 , -80 ) and ( -40 , -50 ) .

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. 2000 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 2000.
  • Every number is a factor of zero (0), since 2000 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, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000 are exact divisors of 2000.
  • Factors of 2000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000. Each factor divides 2000 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000 are all less than or equal to 2000.

Frequently Asked Questions

  • What two numbers make 2000?

    Two numbers that make 2000 are 2 and 1000.

  • What is prime factorization of 2000?

    Prime factorization of 2000 is 2 x 2 x 2 x 2 x 5 x 5 x 5.

  • Write some multiples of 2000?

    First five multiples of 2000 are 4000, 6000, 8000, 10000.

  • Which is the smallest prime factor of 2000?

    The smallest prime factor of 2000 is 2.

  • Is 2000 a perfect square?

    No 2000 is not a perfect square.

  • What is the sum of all factors of 2000?

    The sum of all factors of 2000 is 4836.

  • What are factors of 2000?

    Factors of 2000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000.

  • How do you find factors of a negative number? ( eg. -2000 )?

    Factors of -2000 are -1, -2, -4, -5, -8, -10, -16, -20, -25, -40, -50, -80, -100, -125, -200, -250, -400, -500, -1000, -2000.

  • Is 2000 a whole number?

    Yes 2000 is a whole number.

Examples of Factors

Joy wants to calculate mean of all the factors of 2000. Help him in finding the mean of 2000.

Factors of 2000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 2000 is 1 + 2 + 4 + 5 + 8 + 10 + 16 + 20 + 25 + 40 + 50 + 80 + 100 + 125 + 200 + 250 + 400 + 500 + 1000 + 2000 = 4836.
Hence, the mean of factors of 2000 is 4836 ÷ 20 = 241.80.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 2000? Help her in writing all the factors.

Positive factors are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000.
Negative factors are -1, -2, -4, -5, -8, -10, -16, -20, -25, -40, -50, -80, -100, -125, -200, -250, -400, -500, -1000, -2000.

Joey wants to write all the prime factors of 2000 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 2000 are 2, 2, 2, 2, 5, 5, 5.
So in exponential form it can be written as 24 x 53.

Kevin has been asked to write 19 factor(s) of 2000. Can you predict the answer?

19 factor(s) of 2000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000.

Sammy is puzzled while calculating the prime factors of 2000. Can you help him find them?

Factors of 2000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000.
Prime factors of 2000 are 2, 2, 2, 2, 5, 5, 5

What is prime factorization of 2000?

Prime factorization of 2000 is 2 x 2 x 2 x 2 x 5 x 5 x 5 = 24 x 53.

Can you help Rubel to find out the product of the even factors of 2000?

Factors of 2000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000.
Even factors of 2000 are 2, 4, 8, 10, 16, 20, 40, 50, 80, 100, 200, 250, 400, 500, 1000, 2000.
Hence, product of even factors of 2000 is; 2 x 4 x 8 x 10 x 16 x 20 x 40 x 50 x 80 x 100 x 200 x 250 x 400 x 500 x 1000 x 2000 = 6.5536e+28.