Factors Of 24

Factors of 24 are the integers that can divide the original uniformly. Thus, there will be no remainder left. 24 is a composite number, therefore it will have factors more than two. There are a total of eight factors of 24, they are 1, 2, 3, 4, 6, 8, 12 and 24. Pair factors of 24 are the numbers, which gives the result as 24 when multiplied together in pairs. Its pair factors are (1, 24), (2, 12), (3, 8), and (4, 6). The prime factorisation of 24 gives 2 x 2 x 2 x 3 = 2³ x 3, where 2 and 3 are the prime factors of 24. The sum of factors of 24 is 60. The multiples of 24 are extended times tables, such as, 24, 48, 72, 96, 120, 144, 168, 192, 216, 240, 264, 288, 312, 336, 360 and so on.

What are Factors of 24?

By the definition of factors, we know, a factor can divide a given number into an equal number of parts. Therefore, factors of 24 are such whole numbers that can divide 24 into an equal number of parts.  These factors cannot be a fraction.

How many Factors does 24 have?

By prime factorisation of factors, we get;

 2 x 2 x 2 x 3 = 2³ x 3

We can see here, the exponent of 2 is 3 and 3 is 1.

Now, to find the number of factors of 24 we need to add 1 each to the exponents and multiply them, such as:

(3+1) x (1+1)

= 4 x 2

= 8

Hence, there are 8 positive factors for number 24.

How to Find Factors of 24?

We can easily find the factors of 24 by the division method. As we know, the factors of any number are always less than or equal to the original number. Therefore, we need to divide 24 by a smaller number or by itself. If in the division, the quotient generates is a whole number, then the divisor is the required factor.

1 is the factor of all natural numbers and also a number is a factor of itself. Therefore, 1 and 24 are two factors of 24. Now, 24 is an even number, thus it is divisible by 2. 24/2 = 12, so 2 is a factor. 24 is also a multiple of 3, 4, 6, 8 and 12, therefore the other factors of 24 are 3, 4, 6, 8, and 12. Hence,

• 24 ÷ 1 = 24
• 24 ÷ 2 = 12
• 24 ÷ 3 = 8
• 24 ÷ 4 = 6
• 24 ÷ 6 = 4
• 24 ÷ 8 = 3
• 24 ÷ 12 = 2
• 24 ÷ 24 = 1

Apart from these eight numbers, if we divide 24 by any other number, then the resulting quotient will be a fraction.

For example, 24 ÷ 5 = 4.8

Hence, the calculated factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.

Pair Factors of 24

We can find the factors of number 24, by multiplying two numbers in a pair to get the original number as 24, such as;

• 1 × 24 = 24
• 2 × 12 = 24
• 3 × 8 = 24
• 4 × 6 = 24

Thus, the pair factors are (1, 24), (2, 12), (3, 8), and (4, 6).

We can consider negative pair factors of 24 because the product of two negative factors will result in positive original number, such as:

• -1 × -24 = 24
• -2 × -12 = 24
• -3 × -8 = 24
• -4 × -6 = 24

Thus, the negative pair factors are (-1, -24), (-2, -12), (-3, -8), and (-4, -6).

Prime Factorisation of 24

The number 24 is a composite number. Now let us find the prime factors of 24.

• The first step is to divide the number 24 with the smallest prime factor, i.e. 2.

24 ÷ 2 = 12

Again, divide 12 by 2.

12 ÷ 2 = 6

6 ÷ 2 = 3

• Now, if we divide 3 by 2 we get a fraction number, which cannot be a factor.
• Now, proceed to the next prime numbers, i.e. 3.

3 ÷ 3 = 1

• We have received 1 at the end and further, we cannot proceed with the division method. So, the prime factorisation of 24 is 2 × 2 × 2 × 3 or 2³ × 3, where 2 and 3 are the prime numbers.

Important Points to Remember

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More Factors

Solved Examples on Factors of 24

Q.1: What are the common factors of 24 and 25?

Solution: Common factors between 24 and 25 are given by listing the factors of both numbers.

Factors of 24 = 1, 2, 3, 4, 6, 8, 12 and 24.

Factors of 25 = 1, 5 and 25

Thus, only 1 is the common factor to both the numbers 24 and 25

Q.2: Sam has 24 candies in his pocket. He has to distribute the candies among his 6 friends. How can he do it?

Solution: Number of candies Sam has = 24

Number of friends = 6

Thus, each of the friends will get = 24/6 = 4 candies

Q.3: What are the prime factors of 24?

Solution: The prime factorisation of 24 results in:

24 = 2 × 2 × 2 × 3 or 2³ × 3

Therefore, 2 and 3 are the prime factors of 24.

Factors and Multiples of 24