# Factors of 24

The factors of 24 are the numbers that completely divide 24 without leaving a remainder. Thus we can say that the factors of 24 are the divisors of 24. In this section, we will learn about the factors of 24 and the prime factors of 24.

#### Highlights of Factors of 24

• 24=2×2×2×3 is the prime factorization of 24.
• The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
• 2 and 3 are the prime factors of 24.
• The negative factors of 24 are –1, -2, -3, -4, -6, -8, -12 and –24.

#### What are the factors of 24?

At first, we will find the factors of 24 by the multiplication method. In this method, we need to write the number 24 multiplicatively in all possible ways. We have:

 24 = 1×24 ∴ 1, 24 are factors of 24 24 = 2×12 ∴ 2,12 are factors of 24 24 = 3×8 ∴ 3, 8 are factors of 24 24 = 4×6 ∴ 4, 6 are factors of 24

Note that there are no numbers between 4 and 6 that can divide 24. So we will stop writing 24 multiplicatively. The numbers in violet color are the factors of 24.

∴ we conclude that the factors of 24 are: 1, 2, 3, 4, 6, 8, 12, and 24.

#### Pair Factors of 24

 24 = a×b Pair Factors of 24 24 = 1×24 (1, 24) 24 = 2×12 (2, 12) 24 = 3×8 (3, 8) 24 = 4×6 (4, 6)

Thus the positive pair factors of 24 are (1, 24), (2, 12), (4, 6), and (3, 4). We know that if (a, b) is a positive pair factor of 24, then (-a, -b) is a negative pair factor of 24. Thus, all the negative pair factors of 24 are given below. They are:

(-1, -24), (-2, -12), (-3, -8), and (-4, -6).

#### Number of factors of 24

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

Therefore the total number of factors of 24 is eight.

#### Prime Factors of 24

We have found above that the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. Among those factors, we observe that only 2 and 3 are prime numbers as they do not have any proper divisors.

∴ the prime factors of 24 are 2 and 3.

Question: What are the factors of 24?

Video Solution:

 Factors of 8: 1, 2, 4, 8 Factors of 16: 1, 2, 4, 8, 16 Factors of 20: 1, 2, 4, 5, 10, 20 Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

#### How to find factors of 24?

By division method, we will determine the factors of 24. In this method, we will find the numbers that can divide 24 completely with the remainder zero. See that

 24/1=24 and the remainder is 0. ∴ 1 and 24 are factors of 24. 24/2=12 and the remainder is 0. ∴ 2 and 12 are factors of 24. 24/3=8 and the remainder is 0. ∴ 3 and 8 are factors of 24. 24/4=6 and the remainder is 0. ∴ 4 and 6 are factors of 24.

Note that no numbers other than the numbers in violet color can divide 24. So the numbers in violet color, that is, 1, 2, 3, 4, 6, 8, 12, and 24 are the complete list of factors of 24.