Factors of 24: Prime Factorization, Pair Factors and Factor Tree

Numbers that completely divide 24 and leave no remainders are called factors of 24. The total number of factors of 24 is 8 which are both positive and negative, including two prime numbers. But 24 doesn’t have any decimal or fraction factors. Factors of 24 are simply the numbers that when multiplied by another number give 24 as the product.

Also Read: Real numbers

Key Terms: Factors, Remainder, Prime Factorization, Integers, Decimals, Fractions, Whole Numbers, Prime Numbers, Division

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What are the Factors of 24?

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The factor of a number, let’s say A, is another number, let’s say a, that divides the former one completely with zero as the remainder. Thus:

• Factors of 24 are the numbers that divide it completely.
• Factors of 24 are numbers which when multiplied give 24 as result.

The factors of 24 are 8-8 positive and negative integers.

• Positive Factors: 1, 2, 3, 4, 6, 8, 12, 24
• Negative Factors: -1, -2, -3, -4, -6, -8, -12, -24

Factors of 24

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How to find Factors of 24?

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One can find the factors of 24 by the division method. When dividing 24 by itself or smaller numbers, if the remainder is zero and a quotient is a whole number, the divisor is a factor of 24. Thus, factors of 24 are

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

Except the above divisors, if we 24 is divided by any other number, the quotient will be a fraction. 

Also Read:

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Prime Factorization of 24

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Prime factorizations of a number is defined as an expression where the number is represented through the product of its prime factors. To find the prime factorization of 24 follow the given steps.

• Divide 24 with its smallest prime factor. Here, the smallest prime factor of 24 is 2. So, 24 ÷ 2 = 12
• Repeated division of obtained quotient by 2 until we get a number that is not divisible by 2. Dividing 12 again by 2, 12 ÷ 2 = 6
• 6 is completely divisible by 2, hence, we again perform the division. Thus, 6 ÷ 2 = 3
• Now, dividing the quotient by 3, 3 ÷ 3 = 1

Prime Factorization of 24

Once the quotient is 1, no further division is needed. Thus, the prime factorization of 24 is

2 × 2 × 2 × 3 or 2³ × 3

Also Read: Rational Numbers

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Factor Tree of 24

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Another way of finding the factors of 24 is through the factor tree. The factor tree of any number is drawn by factorization until we reach its prime factors. The steps to draw a factor tree of 24 are as follows.

• The first step is to split 24 into two factors, let’s that be 2 and 12.
• We will circle out 2 as it is one of the prime factors of 12. 
• Moving on to 12 we will further split it into more factors resulting in 2 and 6.
• Again, we will circle 2 and further split 6 into 2 and 3.
• Here we have two prime numbers 2 and 3. 

Factor Tree of 24

When we reach prime factors, the tree is complete. Therefore, the prime factors of 12 are: 

2 x 2 × 2 × 3

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Pair Factors of 24

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24 have both positive and negative factors. The pair of factors which when multiplied gives 24 as the result, is known as the pair factor of 24. There are two types of pair factors: Positive pair factors and Negative pair factors. Both are individually discussed below.

Positive Pair Factor

The table below shows the positive pair factors of 24.

Also Read: Algebra 

Negative Pair Factors

The table below shows the negative pair factors of 24.

Also Read: Geometry

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Solved Examples

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A few solved examples to understand how to use factors of 24 in numerical.

Example 1: Can we divide 24 by 3, 6, 9 and 12 completely?

Solution: The factors of 24 are 1, 2, 3, 4, 6, 12 and 24

Thus only the above-mentioned factors can completely divide 24. 

Hence, 3, 6 and 12 can divide 24 completely but 9 cannot.

Example 2: Find the prime factors of 24.

Solution: Using the prime factorization method, we can find the prime factors of 24.

Following the steps that are mentioned above, the prime factors of 24 are 2 x 2 x 2 x 3.

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Things to Remember

• Factors are defined as the numbers that when dividing another number, leave zero remainders.
• Factors of 24 are the numbers that when multiplied by another number, give 24 as result.
• 24 have 8 positive and 8 negative factors.
• Factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.