What is the Greatest Common Factor of 70 and 84?
Greatest common factor (GCF) of 70 and 84 is 14.
GCF(70,84) = 14
We will now calculate the prime factors of 70 and 84, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 70 and 84.
How to find the GCF of 70 and 84?
We will first find the prime factorization of 70 and 84. After we will calculate the factors of 70 and 84 and find the biggest common factor number .
Step-1: Prime Factorization of 70
Prime factors of 70 are 2, 5, 7. Prime factorization of 70 in exponential form is:
70 = 21 × 51 × 71
Step-2: Prime Factorization of 84
Prime factors of 84 are 2, 3, 7. Prime factorization of 84 in exponential form is:
84 = 22 × 31 × 71
Step-3: Factors of 70
List of positive integer factors of 70 that divides 70 without a remainder.
1, 2, 5, 7, 10, 14, 35
Step-4: Factors of 84
List of positive integer factors of 84 that divides 70 without a remainder.
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42
Final Step: Biggest Common Factor Number
We found the factors and prime factorization of 70 and 84. The biggest common factor number is the GCF number.
So the greatest common factor 70 and 84 is 14.
Also check out the Least Common Multiple of 70 and 84