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How many factors does number 1000 have?

  • Last Updated : 20 Aug, 2021

At the elementary level, factors and multiples are basic concepts that we study together. Factors of a number are defined as the number that gives zero remainders when they divide the specific number. Multiples are the numbers that are multiplied by another number to get the specific number.

In other words, factors of a number, when multiplied by a number, give the original number. Consider we have a number 10, its factors are 2 and 5 as the product of 2 and 5 gives us 10. Other factors of 10 are 10 and 1 as their multiplication also gives us 10.

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The factors of a number can also be negative as the product of two negative numbers is positive, then -1 and -10 are also factors of 10. In total there are 8 factors of 10 i.e., 1, -1, 2, -2, 5, -5, 10, and -10 but only positive factors are considered when solving a problem also fractions are not considered as factors of any number.



Properties of Factors

Factors of a number have certain properties. Some properties of factors are given below:

  • Every number other than 0 and 1 possesses at least two factors.
  • The factor of a given number is always less than the number.
  • The total number of factors of a given number is always finite.
  • To determine factors, division and multiplication are used.

Steps to calculate Factors

To determine the factors of a given number we need to:

  • Write the given number in the terms of the product of two numbers in different ways.
  • All the numbers that are written in these products are the factors of the given number.

What are the factors of 1000?

Solution:

Given that the number is 1000.

Write the number in form of the product of two numbers.

1000 = 1 × 1000



1000 = 2 × 500

1000 = 4 × 250

1000 = 5 × 200

1000 = 8 × 125

1000 = 10 × 100

1000 = 20 × 50

1000 = 25 × 40

All the numbers in the product are factors. Hence, the factors of 1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 250, 500 and 1000. Thus, the total number of factors are 16.

Similar questions

Question 1: Find the factors of 125?

Solution:

Given that the number is 125.

Write the number in the form of the product of two numbers.

125 = 1 × 125

125 = 5 × 25

All the numbers in the product are factors. Hence, the factors are 1, 5, 25 and 125. Thus, the number of factors are 4.

Question 2: Find the factors of 64?

Solution:

Given that the number is 64.

Write the number in the form of the product of two numbers.

64 = 1 × 64



64 = 2 × 32

64 = 4 × 16

64 = 8 × 8

All the numbers in the product are factors. Hence, the factors of 64 are 1, 2, 4, 8, 16, 32 and 64. Thus, the number of factors are 7.

Question 3: Find the factors of 600?

Solution:

Given that the number is 600.

Write the number in the form of the product of two numbers.

600 = 1 × 600

600 = 2 × 300

600 = 3 × 200

600 = 4 × 150

600 = 5 × 120

600 = 6 × 100

600 = 8 × 75

600 = 10 × 60

600 = 12 × 50

600 = 15 × 40

600 = 20 × 30

600 = 24 × 25

All the numbers in the product are factors. Hence, the factors of 600 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300 and 600. Thus, the number of factors are 24.

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