Factors of 48
Methods
What are the Factors of 48?
The following are the different types of factors of 48:
• Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
• Sum of Factors of 48: 124
• Negative Factors of 48: -1, -2, -3, -4, -6, -8, -12, -16, -24, -48
• Prime Factors of 48: 2, 3
• Prime Factorization of 48: 2^4 × 3^1
There are two ways to find the factors of 48: using factor pairs, and using prime factorization.
The Factor Pairs of 48
Factor pairs of 48 are any two numbers that, when multiplied together, equal 48. The question to ask is “what two numbers multiplied together equal 48?” Every factor can be paired with another factor, and multiplying the two will result in 48.
To find the factor pairs of 48, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 48. For reference, the first prime numbers to check are 2, 3, 5, 7, 11, and 13. In this case, the smallest factor that’s a prime number larger than 1 is 2.
Step 2:
Divide 48 by the smallest prime factor, in this case, 2:
48 ÷ 2 = 24
2 and 24 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 24 as the new focus. Find the smallest prime factor that isn’t 1, and divide 24 by that number. In this case, 2 is the new smallest prime factor:
24 ÷ 2 = 12
Remember that this new factor pair is only for the factors of 24, not 48. So, to finish the factor pair for 48, you’d multiply 2 and 2 before pairing with 12:
2 x 2 = 4
Step 4:
Repeat this process until there are no longer any prime factors larger than one to divide by. At the end, you should have the full list of factor pairs.
Here are all the factor pairs for 48:
(1, 48), (2, 24), (3, 16), (4, 12), (6, 8)
So, to list all the factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The negative factors of 48 would be: -1, -2, -3, -4, -6, -8, -12, -16, -24, -48
Prime Factorization of 48
To find the Prime factorization of 48, we break down all the factors of 48 until we are left with only prime factors. We then express n as a product of multiplying the prime factors together.
The process of finding the prime factorization of 48 only has a few differences from the above method of finding the factors of 48. Instead of ensuring we find the right factor pairs, we continue to factor each step until we are left with only the list of smallest prime factors greater than 1.
Here are the steps for finding the prime factorization of 48:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 48. For reference, the first prime numbers to check are 2, 3, 5, 7, 11, and 13. In this case, the smallest factor that’s a prime number larger than 1 is 2.
Step 2:
Divide 48 by the smallest prime factor, in this case, 2
48 ÷ 2 = 24
2 becomes the first number in our prime factorization.
Step 3:
Repeat Steps 1 and 2, using 24 as the new focus. Find the smallest prime factor that isn’t 1, and divide 24 by that number. The smallest prime factor you pick for 24 will then be the next prime factor. If you keep repeating this process, there will be a point where there will be no more prime factors left, which leaves you with the prime factors for prime factorization.
So, the unique prime factors of 48 are: 2, 3
Find the Factors of Other Numbers
Practice your factoring skills by exploring how to factor other numbers, like the ones below:
Factors of 56 - The factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56
Factors of 142 - The factors of 142 are 1, 2, 71, 142
Factors of 9 - The factors of 9 are 1, 3, 9
Factors of 30 - The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30