How to Prime Factors – Practice with Answer Key
- Posted by Brian Stocker MA
- Date April 7, 2014
- Comments 4 comments
How to Prime Factors and Factorization
Factorization or factoring is writing a number or mathematical object as a product of several factors, generally smaller or simpler objects of the same kind.
All about Prime Numbers
What is a prime number?
A prime number is a whole number greater than 1, only divisible by 1 and itself.
What is the first prime number?
The first prime number is 2.
What is a composite number?
A positive integer greater than 1 that is not a prime number.
What is the difference between a prime number and a composite number?
Both prime numbers and composite numbers are positive integers greater than 1. The difference a composite number is not a prime number.
Prime Factors Practice Questions
1. What are the prime factors of 17?
a. 2 x 8.5
b. 17
c. 3 x 5.5
d. None of the above
2. What are the prime factors of 100?
a. 2 x 2 x 5 x 5
b. 4 x 25
c. 2 x 2 x 2 x 5 x 5
d. 2 x 50
3. What are the prime factors of 25?
a. 4 x 5.5
b. 5 x 5 x 5
c. 1 x 25
d. 5 x 5
4. What are the prime factors of 81?
a. 3 x 3 x 9
b. 3 x 27
c. 3 x 3 x 3 x 3
d. All of the above
5. What are the prime factors of 125?
a. 5 x 25
b. 5 x 5 x 5
c. All of the above
d. None of the above
6. What are the prime factors of 132?
a. 4 x 3 x 11
b. 2 x 2 x 2 x 3 x 11
c. 2 x 6 x 11
d. 2 x 2 x 3 x 11
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Answer Key
1. B
The only prime number that can divide 17 is 17.
2. A
To make it easier we can break this large number to two smaller numbers, 2 x 50 or 4 x 25. Let’s use 4 x 25. The prime factors of 4 = 2 x 2, and the prime factors of 25 = 5 x 5. The prime factors of 100 = 2 x 2 x 5 x 5.
3. D
The smallest prime number that can divide 25 is 5. 25/5 = 5. Prime factors of 25 = 5 x 5.
4. C
To make this easier we can break 81 to be 9 x 9 and then find the prime factors of each of these prime numbers. The prime factors of 9 = 3 x 3 and the prime factors of 9 = 3 x 3 Prime factors of 81 = 3 x 3 x 3 x 3.
5. B
The smallest prime number that can divide 125 is 5. 125/5 = 25. 25/5 =5. Prime factors of 125 = 5 x 5 x5
6. D
The smallest prime number to divide 132 is 2. 132/2 = 66. 66/2 = 33. 33/3 = 11. 11 cannot be divided further by a prime number other than 11. The prime numbers of 132 = 2 x 2 x 3 x 11.
Date Published: Monday, April 7th, 2014
Date Modified: Thursday, April 18th, 2024
4 Comments
this is a good website because it gives us extra practice for the test that’s coming up or soon.
Thank-you for posting this, it’s really helpful
it was a nice experience for me to correct my mistakes. Thanks for the one who prepared
Can you explain #5 better?