What is the Greatest Common Factor of 70 and 75?
Greatest common factor (GCF) of 70 and 75 is 5.
GCF(70,75) = 5
We will now calculate the prime factors of 70 and 75, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 70 and 75.
How to find the GCF of 70 and 75?
We will first find the prime factorization of 70 and 75. After we will calculate the factors of 70 and 75 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 75
Prime factors of 75 are 3, 5. Prime factorization of 75 in exponential form is:
75 = 31 × 52
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 75
List of positive integer factors of 75 that divides 70 without a remainder.
1, 3, 5, 15, 25
Final Step: Biggest Common Factor Number
We found the factors and prime factorization of 70 and 75. The biggest common factor number is the GCF number.
So the greatest common factor 70 and 75 is 5.
Also check out the Least Common Multiple of 70 and 75