How to Solve Prime Factor Questions – 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.
Tips for Solving Prime Number Questions
1. Understand Prime Factors
Prime factors are the prime numbers that multiply. For example, the prime factors of 28 are 2 and 7, 2 × 2 × 7 = 28
2. Start with the Smallest Prime Number
Start by dividing the number by the smallest prime, which is 2, and continue dividing by 2 until you can’t divide evenly.
3. Move to the Next Prime Number
Here, once 2 no longer divides evenly, try the next smallest prime number, 3.
4. Repeat Repeat
Repeat with subsequent primes (here, 5, 7, 11, 13, etc.) until the quotient is 1.
5. Use a Prime Number Lists
Use a list – see Wikipedia List of Primes
6. Check Your Work
Good advice for any question! Make sure the primes you found multiply to the answer.
Tips for Efficiency
Memorize Small Primes The first few primes (2, 3, 5, 7, 11, 13, 17, 19, 23, 29) will allow you to answer faster.
Recognize Patterns: For example, even numbers are always divisible by 2, and numbers ending in 0 or 5 are divisible by 5.
Use Division Rules: Know the rules for divisibility to quickly identify factors. For example, a number is divisible by 3 if the sum of its digits is divisible by 3.
Factor Trees: Draw a factor tree to break down the number into primes.
Date Published: Monday, April 7th, 2014
Date Modified: Friday, June 14th, 2024
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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?