What is the Greatest Common Factor of 705 and 715?

Greatest common factor (GCF) of 705 and 715 is 5.

GCF(705,715) = 5

We will now calculate the prime factors of 705 and 715, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 705 and 715.

How to find the GCF of 705 and 715?

We will first find the prime factorization of 705 and 715. After we will calculate the factors of 705 and 715 and find the biggest common factor number .

Step-1: Prime Factorization of 705

Prime factors of 705 are 3, 5, 47. Prime factorization of 705 in exponential form is:

705 = 3¹ × 5¹ × 47¹

Step-2: Prime Factorization of 715

Prime factors of 715 are 5, 11, 13. Prime factorization of 715 in exponential form is:

715 = 5¹ × 11¹ × 13¹

Step-3: Factors of 705

List of positive integer factors of 705 that divides 705 without a remainder.

1, 3, 5, 15, 47, 141, 235

Step-4: Factors of 715

List of positive integer factors of 715 that divides 705 without a remainder.

1, 5, 11, 13, 55, 65, 143

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 705 and 715. The biggest common factor number is the GCF number.
So the greatest common factor 705 and 715 is 5.

Also check out the Least Common Multiple of 705 and 715