MATH SOLVE

4 months ago

Q:
# What are the Factors of 35?

Accepted Solution

A:

Factors of 35
Methods
What are the Factors of 35?
The following are the different types of factors of 35:
• Factors of 35: 1, 5, 7, 35
• Sum of Factors of 35: 48
• Negative Factors of 35: -1, -5, -7, -35
• Prime Factors of 35: 5, 7
• Prime Factorization of 35: 5^1 × 7^1
There are two ways to find the factors of 35: using factor pairs, and using prime factorization.
The Factor Pairs of 35
Factor pairs of 35 are any two numbers that, when multiplied together, equal 35. The question to ask is “what two numbers multiplied together equal 35?” Every factor can be paired with another factor, and multiplying the two will result in 35.
To find the factor pairs of 35, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 35. 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 5.
Step 2:
Divide 35 by the smallest prime factor, in this case, 5:
35 ÷ 5 = 7
5 and 7 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 7 as the new focus. Find the smallest prime factor that isn’t 1, and divide 7 by that number. In this case, 7 is the new smallest prime factor:
7 ÷ 7 = 1
Remember that this new factor pair is only for the factors of 7, not 35. So, to finish the factor pair for 35, you’d multiply 5 and 7 before pairing with 1:
5 x 7 = 35
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 35:
(1, 35), (5, 7)
So, to list all the factors of 35: 1, 5, 7, 35
The negative factors of 35 would be: -1, -5, -7, -35
Prime Factorization of 35
To find the Prime factorization of 35, we break down all the factors of 35 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 35 only has a few differences from the above method of finding the factors of 35. 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 35:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 35. 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 5.
Step 2:
Divide 35 by the smallest prime factor, in this case, 5
35 ÷ 5 = 7
5 becomes the first number in our prime factorization.
Step 3:
Repeat Steps 1 and 2, using 7 as the new focus. Find the smallest prime factor that isn’t 1, and divide 7 by that number. The smallest prime factor you pick for 7 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 35 are: 5, 7
Find the Factors of Other Numbers
Practice your factoring skills by exploring how to factor other numbers, like the ones below:
Factors of 94 - The factors of 94 are 1, 2, 47, 94
Factors of 1 - The factors of 1 are 1
Factors of 109 - The factors of 109 are 1, 109
Factors of 135 - The factors of 135 are 1, 3, 5, 9, 15, 27, 45, 135