Loading…
Factors of 75: As Taught by a Math Tutor
Methods
What are the Factors of 75?
As your math tutor, I’m here to guide you through the different types of factors of 75. Understanding factors is key to mastering multiplication, division, and prime numbers. Here’s a breakdown:
• Factors of 75: 1, 3, 5, 15, 25, 75
• Sum of Factors of 75: 124
• Negative Factors of 75: -1, -3, -5, -15, -25, -75
• Prime Factors of 75: 3, 5
• Prime Factorization of 75: 3^1 × 5^2
There are two main ways a math tutor would explain how to find the factors of 75: using factor pairs and prime factorization. Let’s explore both!
The Factor Pairs of 75
As your math tutor, I’m here to help you break down factor pairs of 75 step by step!
Factor pairs of 75 are any two numbers that, when multiplied together, equal 75. The question to ask is “what two numbers multiplied together equal 75?” Every factor can be paired with another factor, and multiplying the two will result in 75.
To find the factor pairs of 75, follow these steps:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 75. 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 75 by the smallest prime factor, in this case, 3:
75 ÷ 3 = 25
3 and 25 will make a new factor pair.
Step 3:
Repeat Steps 1 and 2, using 25 as the new focus. Find the smallest prime factor that isn’t 1, and divide 25 by that number. In this case, 5 is the new smallest prime factor:
25 ÷ 5 = 5
Remember that this new factor pair is only for the factors of 25, not 75. So, to finish the factor pair for 75, you’d multiply 3 and 5 before pairing with 5:
3 x 5 = 15
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 75:
(1, 75), (3, 25), (5, 15)
So, to list all the factors of 75: 1, 3, 5, 15, 25, 75
The negative factors of 75 would be: -1, -3, -5, -15, -25, -75
Now you’ve got it! A math tutor would always encourage you to practice with different numbers to reinforce your understanding of factor pairs. Try another one!
Prime Factorization of 75
To find the prime factorization of 75, we break it down step by step until only prime factors remain. Then, we express 75 as a product of these prime factors multiplied together. Let’s go through the process and simplify it like a math tutor would!
The process of finding the prime factorization of 75 only has a few differences from the above method of finding the factors of 75. 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 75:
Step 1:
Find the smallest prime number that is larger than 1, and is a factor of 75. 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 75 by the smallest prime factor, in this case, 3
75 ÷ 3 = 25
3 becomes the first number in our prime factorization.
Step 3:
Repeat Steps 1 and 2, using 25 as the new focus. Find the smallest prime factor that isn’t 1, and divide 25 by that number. The smallest prime factor you pick for 25 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 75 are: 3, 5
Math Tutor Suggests: Find the Factors of Other Numbers
Practice your factoring skills by exploring how to factor other numbers, like the ones below:
Factors of 26 - The factors of 26 are 1, 2, 13, 26
Factors of 136 - The factors of 136 are 1, 2, 4, 8, 17, 34, 68, 136
Factors of 15 - The factors of 15 are 1, 3, 5, 15
Factors of 142 - The factors of 142 are 1, 2, 71, 142
Download FREE Math Resources
Take advantage of our free downloadable resources and study materials for at-home learning.
8 Math Hacks and Tricks to Turn Your 'Okay' Math Student Into a Math Champion!
One thing we teach our students at Thinkster is that there are multiple ways to solve a math problem. This helps our students learn to think flexibly and non-linearly.
Get PDF
Math Tutoring to Boost Your Child’s Math Skills & Scores by 90% in Just 3 Months – Guaranteed!
Does your child struggle with math homework or understanding tricky math concepts? Do they do okay in math, but express excitement to learn new material or advanced math?
A Thinkster Math tutor provides one-to-one support to help elementary, middle school, and high school students build confidence and master math subjects like K-8 math, pre-algebra, algebra, geometry, calculus, and more.
Our expert math tutors customize math lessons to your child’s unique needs, making learning math fun and effective. We help students improve grades, develop strong critical thinking skills through solving word problems, excel in standardized tests, and develop strong problem-solving skills.
Our expert math tutors are ready to help make your child a champion and develop strong math mastery! Sign up for our 7-day free trial and get the best math tutor for your child today!
Start 7-Day Free Trial