What is the Greatest Common Factor of 42 and 60?
Greatest common factor (GCF) of 42 and 60 is 6.
GCF(42,60) = 6
We will now calculate the prime factors of 42 and 60, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 42 and 60.
How to find the GCF of 42 and 60?
We will first find the prime factorization of 42 and 60. After we will calculate the factors of 42 and 60 and find the biggest common factor number .
Step-1: Prime Factorization of 42
Prime factors of 42 are 2, 3, 7. Prime factorization of 42 in exponential form is:
42 = 21 × 31 × 71
Step-2: Prime Factorization of 60
Prime factors of 60 are 2, 3, 5. Prime factorization of 60 in exponential form is:
60 = 22 × 31 × 51
Step-3: Factors of 42
List of positive integer factors of 42 that divides 42 without a remainder.
1, 2, 3, 6, 7, 14, 21
Step-4: Factors of 60
List of positive integer factors of 60 that divides 42 without a remainder.
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30
Final Step: Biggest Common Factor Number
We found the factors and prime factorization of 42 and 60. The biggest common factor number is the GCF number.
So the greatest common factor 42 and 60 is 6.
Also check out the Least Common Multiple of 42 and 60