# Factors of 20

What are the factors of 20? The factors of 20 are the numbers that completely divide 20 without leaving a remainder. Thus we can say that the factors of 20 are the divisors of 20. In this section, we will learn about the factors of 20 and the prime factors of 20.

#### Highlights of Factors of 20

• 20=2×2×5 is the prime factorization of 20.
• The factors of 20 are 1, 2, 4, 5, 10, and 20.
• 2 is the only prime factor of 20.
• The negative factors of 20 are -1, -2, -4, -5, -10 and -20.

#### What are the factors of 20?

To get the factors of 20 by the multiplication method, we will first write the number 20 multiplicatively in all possible ways. We can write 20 as follows and we have:

 20 = 1×20 ∴ 1, 20 are factors of 20 20 = 2×10 ∴ 2, 10 are factors of 20 20 = 4×5 ∴ 4, 5 are factors of 20

Note that we cannot express 20 multiplicatively in any way other than the above ones, so we will stop now. Hence the factors of 20 are the numbers in brown color.

∴ the factors of 20 are 1, 2, 4, 5, 10, and 20.

We know that if m is a factor of 20, then -m is also a factor of 20. Using this fact we get all the negative factors of 20 and they are -1, -2, -4, -5, -10, and -20.

#### Pair Factors of 20

 20 = a×b Factors in Pairs (a,b) 20 = 1×20 (1, 20) 20 = 2×10 (2, 10) 20 = 4×5 (4, 5)

Thus the pair factors of 20 are (1, 20), (2, 10), and (4, 5).

We know that (m, n) is a positive pair factor of 20 if and only if (-m, -n) is a negative pair factor of 20. Thus, all the negative pair factors of 20 are (-1, -20), (-2, -10) and (-4, -5).

#### Number of factors of 20

The factors of 20 are 1, 2, 4, 5, 10, and 20.

Therefore the total number of factors of 20 is six.

#### Prime Factors of 20

We have found above that the factors of 20 are 1, 2, 4, 5, 10, and 20. Among those factors, we observe that only 2 is the prime number as it does not have any proper divisors.

∴ the only prime factor of 20 is 2.

Question: What are the factors of 20?

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