MATH SOLVE

4 months ago

Q:
# What are the Factors of 264?

Accepted Solution

A:

Factors of 264
Methods
What are the Factors of 264?
The following are the different types of factors of 264:
• Factors of 264: 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264
• Sum of Factors of 264: 720
• Negative Factors of 264: -1, -2, -3, -4, -6, -8, -11, -12, -22, -24, -33, -44, -66, -88, -132, -264
• Prime Factors of 264: 2, 3, 11
• Prime Factorization of 264: 2^3 × 3^1 × 11^1
There are two ways to find the factors of 264: using factor pairs, and using prime factorization.
The Factor Pairs of 264
Factor pairs of 264 are any two numbers that, when multiplied together, equal 264. The question to ask is “what two numbers multiplied together equal 264?” Every factor can be paired with another factor, and multiplying the two will result in 264.
To find the factor pairs of 264, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 264. 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 264 by the smallest prime factor, in this case, 2:
264 ÷ 2 = 132
2 and 132 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 132 as the new focus. Find the smallest prime factor that isn’t 1, and divide 132 by that number. In this case, 2 is the new smallest prime factor:
132 ÷ 2 = 66
Remember that this new factor pair is only for the factors of 132, not 264. So, to finish the factor pair for 264, you’d multiply 2 and 2 before pairing with 66:
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 264:
(1, 264), (2, 132), (3, 88), (4, 66), (6, 44), (8, 33), (11, 24), (12, 22)
So, to list all the factors of 264: 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264
The negative factors of 264 would be: -1, -2, -3, -4, -6, -8, -11, -12, -22, -24, -33, -44, -66, -88, -132, -264
Prime Factorization of 264
To find the Prime factorization of 264, we break down all the factors of 264 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 264 only has a few differences from the above method of finding the factors of 264. 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 264:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 264. 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 264 by the smallest prime factor, in this case, 2
264 ÷ 2 = 132
2 becomes the first number in our prime factorization.
Step 3:
Repeat Steps 1 and 2, using 132 as the new focus. Find the smallest prime factor that isn’t 1, and divide 132 by that number. The smallest prime factor you pick for 132 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 264 are: 2, 3, 11
Find the Factors of Other Numbers
Practice your factoring skills by exploring how to factor other numbers, like the ones below:
Factors of 36 - The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 140 - The factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
Factors of 147 - The factors of 147 are 1, 3, 7, 21, 49, 147
Factors of 90 - The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90