What is the Greatest Common Factor of 706 and 725?

Greatest common factor (GCF) of 706 and 725 is 1.

GCF(706,725) = 1

We will now calculate the prime factors of 706 and 725, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 706 and 725.

How to find the GCF of 706 and 725?

We will first find the prime factorization of 706 and 725. After we will calculate the factors of 706 and 725 and find the biggest common factor number .

Step-1: Prime Factorization of 706

Prime factors of 706 are 2, 353. Prime factorization of 706 in exponential form is:

706 = 2¹ × 353¹

Step-2: Prime Factorization of 725

Prime factors of 725 are 5, 29. Prime factorization of 725 in exponential form is:

725 = 5² × 29¹

Step-3: Factors of 706

List of positive integer factors of 706 that divides 706 without a remainder.

1, 2, 353

Step-4: Factors of 725

List of positive integer factors of 725 that divides 706 without a remainder.

1, 5, 25, 29, 145

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 706 and 725. The biggest common factor number is the GCF number.
So the greatest common factor 706 and 725 is 1.

Also check out the Least Common Multiple of 706 and 725