Factors of 48

Factors of 48 are the list of integers that can be evenly divided into 48. It has a total of 10 factors of which 48 is the biggest factor and the prime factors of 48 are 2 and 3. The Prime Factorization of 48 is 2⁴ × 3.

• Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48
• Negative Factors of 48: -1, -2, -3, -4, -6, -8, -12, -16, -24 and -48
• Prime Factors of 48: 2, 3
• Prime Factorization of 48: 2 × 2 × 2 × 2 × 3 = 2⁴ × 3
• Sum of Factors of 48: 124

What Are the Factors of 48?

Factors of 48 are the numbers that, when multiplied together, result in 48.

6 × 8 = 48

48/8=6

Here 6 and 8 are multiplied together to get 48.

Hence, we say that 6 and 8 are the factors of 48.

48 has many other factors too as 6 and 8 have factors themselves.

To find them, you can arrange these numbers in arrays as follows.

You may arrange 48 in arrays as above and find the factors of 48.

How to Calculate the Factors of 48?

Step 1: Write down the number to be factored, i.e., 48.

It is a composite number. It can be factored further.

Step 2: Find the two numbers whose product gives 48.

2 × 24 = 48. So, let's take 2 and 24 as the two factors.

2 is a prime number. Hence, it can only be factored as 1 and the number itself.

1 × 2 = 2

Step 3: Since 24 is not prime, let's break it down into factors.

2 × 12 = 24. So, let's take 2 and 12 as the two factors.

Again, 2 is a prime number.

Step 4: Break 12 into factors.

3 × 4 = 12

2 is a prime number.

Step 5: Break 4 into factors.

2 × 2 = 4

We stop here as we have found all the factors of 48.

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

Tips and Tricks:

1. 1 is the smallest factor of every number.
2. Every number has a minimum of 2 factors, i.e., 1 and the number itself.
3. All even numbers always have 2 as one of their factors.

Explore factors using illustrations and interactive examples.

• Factors of 36 - The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
• Factors of 24 - The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
• Factors of 15 - The factors of 15 are 1, 3, 5, 15
• Factors of 45 - The factors of 45 are 1, 3, 5, 9, 15, 45
• Factors of 72 - The factors of 72 are 1, 2, 3, 4, 6, 8, 9 12, 18, 24, 36, 72
• Factors of 49 - The factors of 49 are 1, 7, 49

Factors of 48 by Prime Factorization

If the factors of a number are prime numbers, then the factors are said to be prime factors.

Prime factorization is the process of writing a number as a product of its prime factors.
Factors of 48 by prime factorization are given using the following steps.

Step 1: Write the pair of factors that, on multiplication, give the required number.
48 can be factored as a product of 6 and 8.

Step 2: See the factors, whether each one of them is prime or not.
6 is not a prime number and can be factored in as a product of 2 and 3.
8 is not a prime number and can be factored in as a product of 2 and 4.
4 is not a prime number and can be factored in as a product of 2 and 2.

Step 3: As per the criterion,
48 can thereby be written as:
48 = 6 × 8 = 2 × 3 × 2 × 2 × 2
It can also be written as:
48 = 2⁴ × 3¹

We can also find the prime factors by this division method or the factor tree method.

Factors of 48 by Division Method

We divide the number every time in such a way that a divisor is a prime number as below.

48 = 2⁴ × 3

Factors of 48 by Factor Tree Method

Can you draw the tree in a quite different way?

Finally, you will get the same prime factorization as 48= 2⁴ × 3¹

Challenging Questions:

What are the factors of the following numbers using the prime factorization method?

1. 96
2. 245
3. 6400

Factors of 48 in Pairs

Factor pairs are found in this rainbow method.

Positive Pair Factors of 48

Negative Pair Factors of 48

Important Notes:

• Factors of any number are all the possible divisible numbers. They may be prime numbers or composite numbers.
• Factors are never fractions or decimals.
• Factors can be negative.