MATH SOLVE

3 months ago

Q:
# What are the Factors of 45?

Accepted Solution

A:

Factors of 45
Methods
What are the Factors of 45?
The following are the different types of factors of 45:
• Factors of 45: 1, 3, 5, 9, 15, 45
• Sum of Factors of 45: 78
• Negative Factors of 45: -1, -3, -5, -9, -15, -45
• Prime Factors of 45: 3, 5
• Prime Factorization of 45: 3^2 × 5^1
There are two ways to find the factors of 45: using factor pairs, and using prime factorization.
The Factor Pairs of 45
Factor pairs of 45 are any two numbers that, when multiplied together, equal 45. The question to ask is “what two numbers multiplied together equal 45?” Every factor can be paired with another factor, and multiplying the two will result in 45.
To find the factor pairs of 45, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 45. 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 3.
Step 2:
Divide 45 by the smallest prime factor, in this case, 3:
45 ÷ 3 = 15
3 and 15 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 15 as the new focus. Find the smallest prime factor that isn’t 1, and divide 15 by that number. In this case, 3 is the new smallest prime factor:
15 ÷ 3 = 5
Remember that this new factor pair is only for the factors of 15, not 45. So, to finish the factor pair for 45, you’d multiply 3 and 3 before pairing with 5:
3 x 3 = 9
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 45:
(1, 45), (3, 15), (5, 9)
So, to list all the factors of 45: 1, 3, 5, 9, 15, 45
The negative factors of 45 would be: -1, -3, -5, -9, -15, -45
Prime Factorization of 45
To find the Prime factorization of 45, we break down all the factors of 45 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 45 only has a few differences from the above method of finding the factors of 45. 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 45:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 45. 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 3.
Step 2:
Divide 45 by the smallest prime factor, in this case, 3
45 ÷ 3 = 15
3 becomes the first number in our prime factorization.
Step 3:
Repeat Steps 1 and 2, using 15 as the new focus. Find the smallest prime factor that isn’t 1, and divide 15 by that number. The smallest prime factor you pick for 15 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 45 are: 3, 5
Find the Factors of Other Numbers
Practice your factoring skills by exploring how to factor other numbers, like the ones below:
Factors of 75 - The factors of 75 are 1, 3, 5, 15, 25, 75
Factors of 94 - The factors of 94 are 1, 2, 47, 94
Factors of 110 - The factors of 110 are 1, 2, 5, 10, 11, 22, 55, 110
Factors of 78 - The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78