How To Find The Prime Factors Of 48 By Prime Factorization Method?

Factors of 48 are the numbers that give the original number when multiplied together in pairs or we can say, the numbers which divide 48 completely, leaving zero as a remainder, are its factors. The factors of 48 can be positive or negative. For example, the factors of 48 can be (1, 48) or (-1, -48). If we multiply the pair of negative factors, such as multiplying -1 and -48, it will result in the original number 48. Here, we will learn the factors of 48 and the pair factors and the prime factors of 48 using the prime factorization method with many solved examples. 

Table of Contents:

• What are the Factors of 48?
• Pair Factors of 48
• Factors of 48 by Division Method
• Prime Factorization of 48
• Solved Examples
• FAQs

What are the Factors of 48?

The factors of 48 are the numbers that divide 48 exactly without leaving any remainder. In other words, the factors of 48 are the numbers that are multiplied in pairs resulting in an original number. As 48 is an even composite number, 48 has many factors other than 1 and 48. Thus, the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.

Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48. Prime Factorization of 48: 2×2×2×2×3 or 24 × 3.

Pair Factors of 48

The pair factors of 48 are the numbers in which the pair of numbers are multiplied together resulting in an original number 48. As discussed above, the pair factors of 48 can also be positive or negative. Thus, the positive and negative pair factors of 48 are given below:

Positive Pair Factors of 48:

Positive Factors of 48	Positive Pair Factors of 48
1 × 48	(1, 48)
2 × 24	(2, 24)
3 × 16	(3, 16)
4 × 12	(4, 12)
6 × 8	(6, 8)

Negative Pair Factors of 48:

Negative Factors of 48	Negative Pair Factors of 48
-1 × -48	(-1, -48)
-2 × -24	(-2, -24)
-3 × -16	(-3, -16)
-4 × -12	(-4, -12)
-6 × -8	(-6, -8)

Factors of 48 by Division Method

In the division method, the factors of 48 can be found by dividing 48 by different consecutive integers. If the integer divides 48 exactly and leaves the remainder 0, then the integers are the factors of 48. Now, let us discuss how to find the factors of the division method.

• • • 48/1 = 48 (Factor 1 and Remainder = 0)
    • 48/2 = 24 (Factor 2 and Remainder = 0)
    • 48/3 = 16 (Factor 3 and Remainder =0)
    • 48/4 = 12 (Factor 4 and Remainder =0)
    • 48/6 = 8 (Factor 6 and Remainder =0)
    • 48/8 =6 (Factor =8 and Remainder =0)
    • 48/12 = 4 (Factor =12 and Remainder =0)
    • 48/16 = 3 (Factor = 16 and Remainder =0)
    • 48/24 = 2 (Factor = 24 and Remainder =0)
    • 48/48 = 1 (Factor = 48 and Remainder =0)

Thus, the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.

If we divide 48 by any numbers other than 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48, it leaves a remainder, and hence, they are not the factors of 48.

Prime Factorization of 48

The number 48 is a composite number. Now let us find the prime factorisation of it.

• • • The first step is to divide the number 48 with the smallest prime factor,i.e. 2.

48 ÷ 2 = 24

• • • Now, check whether 24 can be further divided by 2 or not.

24 ÷ 2 = 12

12 ÷ 2 = 6

6 ÷ 2 = 3

• • • As 3 cannot be divided by 2 because factors are the whole numbers and not the fraction.
    • Therefore, we need to divide 3 by 3 itself, as 3 is the next prime number.

3 ÷ 3 = 1

• • • We have received 1 at the end and further, we cannot proceed with the division method. So, the prime factors of 48 are 2 × 2 × 2 × 2 × 3 or we can also write them as 24 × 3, where 2 and 3 both are prime numbers.

Video Lesson on Prime Factors

Links Related to Factors
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Examples

Example 1:

Find the common factors of 48 and 47.

Solution:

The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.

The factors of 47 are 1 and 47.

As 47 is a prime number, the common factor of 47 and 48 is 1.

Example 2:

Find the common factors of 48 and 49.

Solution:

Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.

Factors of 49 = 1, 7, and 49.

Thus, the common factor of 48 and 49 is 1.

Example 3:

Find the common factors of 48 and 24.

Solution:

The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.

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

Hence, the common factors of 48 and 24 are 1, 2, 3, 4, 6, 8, 12 and 24

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Frequently Asked Questions on Factors of 48

Q1

What are the factors of 48?

The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.

Q2

What is the prime factorization of 48?

The prime factorization of 48 is 2×2×2×2×3 or 24 × 3.

Q3

Write down the positive pair factors of 48?

The positive pair factors of 48 are (1, 48), (2, 24), (3, 16), (4, 12), and (6, 8).

Q4

What are the negative pair factors of 48?

The negative pair factors of 48 are (-1, -48), (-2, -24), (-3, -16), (-4, -12), and (-6, -8).

Q5

Is 24 a factor of 48?

Yes, 24 is a factor of 48. If 48 is divided by 24, it leaves a remainder 0, and hence 24 is a factor of 48.

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