GCD via Prime Factorization: Efficient Methods and Practice

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1) Find the GCD of 18 and 24 using prime factorization.

18=2×3×3; 24=2×2×2×3; Common=2×3=6.

Explanation

18=2×3×3; 24=2×2×2×3; Common=2×3=6.

About This Quiz

Want to see how prime numbers connect to the GCD? In this quiz, you’ll break numbers into prime factors and use those building blocks to find the greatest common divisor. You’ll practice step by step and discover how prime factorization makes GCD calculations easier. Take this quiz if you’re ready... see morefor a deeper look at how primes rule the math world.
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2) Prime factorization of 60 = 2×2×3×5. Prime factorization of 90 = 2×3×3×5. What is the GCD?

Common=2×3×5=30.

Explanation

Common=2×3×5=30.

3) Find the GCD of 45 and 120 using prime factors.

45=3×3×5; 120=2×2×2×3×5; Common=3×5=15.

Explanation

45=3×3×5; 120=2×2×2×3×5; Common=3×5=15.

4) Prime factors of 50 are 2×5×5. Prime factors of 75 are 3×5×5. What is the GCD?

Common=5×5=25.

Explanation

Common=5×5=25.

5) Find the GCD of 64 and 96.

The greatest common divisor (GCD) of two numbers is the largest number that divides both of them without leaving a remainder. For 64 and 96, the factors of 64 are 1, 2, 4, 8, 16, 32, and 64. The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96. The largest common factor between these two sets is 32.

Explanation

6) The GCD of 36 and 60 is:

36=2×2×3×3; 60=2×2×3×5; Common=2×2×3=12.

Explanation

36=2×2×3×3; 60=2×2×3×5; Common=2×2×3=12.

7) The GCD of 48 and 72 is:

48=2×2×2×2×3; 72=2×2×2×3×3; Common=2×2×2×3=24.

Explanation

48=2×2×2×2×3; 72=2×2×2×3×3; Common=2×2×2×3=24.

8) Prime factorization of 84 = 2×2×3×7. Prime factorization of 126 = 2×3×3×7. What is the GCD?

Common=2×3×7=42.

Explanation

Common=2×3×7=42.

9) The GCD of 100 and 140 is:

100=2×2×5×5; 140=2×2×5×7; Common=2×2×5=20.

Explanation

100=2×2×5×5; 140=2×2×5×7; Common=2×2×5=20.

10) Prime factorization of 27 = 3×3×3. Prime factorization of 36 = 2×2×3×3. What is the GCD?

Common=3×3=9.

Explanation

Common=3×3=9.

Thank you for your feedback!

Cierra Henderson |MBA |

K-12 Expert

Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.