# Factors of 10

Definition of factors of 10: If a number completely divides 10 with the remainder zero, then that number is called a factor of 10. So we can say that the factors of 10 are the divisors of 10. In this section, we will learn about the factors of 10 and the prime factors of 10.

#### Highlights of Factors of 10

• 10=2×5 is the prime factorization of 10.
• The factors of 10 are 1, 2, 5, and 10.
• Prime factors of 10 are 2 and 5.
• Negative factors of 10 are -1, -2, -5 and -10.

#### What are the factors of 10?

Let us write the number 10 multiplicatively in all possible ways. We have:

 10 = 1×10 ∴ 1, 10 are factors of 10 10 = 2×5 ∴ 2, 5 are factors of 10

We cannot express 10 multiplicatively in any other way. So we will stop now. Note that the numbers in brown color are the factors of 10.

∴ All the factors of 10 are 1, 2, 5, and 10.

We know that if m is a factor of 16, then -m is also a factor of 16. Thus all the negative factors of 10 are -1, -2, -5, and -10.

#### Pair Factors of 10

 10 = a×b Factors in Pairs (a,b) 10 = 1×10 (1, 10) 10 = 2×5 (2, 5)

Thus the pair factors of 10 are (1, 10) and (2, 5).

We know that if (a, b) is a positive pair factor of 10, then (-a, -b) is a negative pair factor of 10. Thus, all the negative pair factors of 16 are (-1, -10) and (-2, -5).

#### Number of factors of 10

From above we have calculated the factors of 10 which are 1, 2, 5, and 10. Thus the total number of factors of 10 is four.

#### Prime Factors of 10

Note that the factors of 10 are 1, 2, 5, and 10. Among those factors, we observe that 2 and 5 are prime numbers as they do not have any proper divisors.

∴ the prime factors of 10 are 2 and 5.

 Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 Factors of 20: 1, 2, 4, 5, 10, 20 Factors of 27: 1, 3, 9, 27

Question: What are the factors of 10?

Video Solution:

#### How to find factors of 10?

Now we will determine the factors of 10 by division method. In this method, we will find the numbers that can divide 10 with no remainder. See that

 10/1=10 and the remainder is 0 ∴ 1 and 10 are factors of 10 10/2=5 and the remainder is 0 ∴ 2 and 5 are factors of 10

Note that no numbers other than the numbers in violet color can divide 10. So the numbers in violet color, that is, 1, 2, 5 and 10 are the complete list of factors of 10.