What is the Greatest Common Factor of 21 and 34?
Greatest common factor (GCF) of 21 and 34 is 1.
GCF(21,34) = 1
We will now calculate the prime factors of 21 and 34, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21 and 34.
How to find the GCF of 21 and 34?
We will first find the prime factorization of 21 and 34. After we will calculate the factors of 21 and 34 and find the biggest common factor number .
Step-1: Prime Factorization of 21
Prime factors of 21 are 3, 7. Prime factorization of 21 in exponential form is:
21 = 31 × 71
Step-2: Prime Factorization of 34
Prime factors of 34 are 2, 17. Prime factorization of 34 in exponential form is:
34 = 21 × 171
Step-3: Factors of 21
List of positive integer factors of 21 that divides 21 without a remainder.
1, 3, 7
Step-4: Factors of 34
List of positive integer factors of 34 that divides 21 without a remainder.
1, 2, 17
Final Step: Biggest Common Factor Number
We found the factors and prime factorization of 21 and 34. The biggest common factor number is the GCF number.
So the greatest common factor 21 and 34 is 1.
Also check out the Least Common Multiple of 21 and 34