What is the Greatest Common Factor of 71739 and 71757?

Greatest common factor (GCF) of 71739 and 71757 is 9.

GCF(71739,71757) = 9

We will now calculate the prime factors of 71739 and 71757, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71739 and 71757.

How to find the GCF of 71739 and 71757?

We will first find the prime factorization of 71739 and 71757. After we will calculate the factors of 71739 and 71757 and find the biggest common factor number .

Step-1: Prime Factorization of 71739

Prime factors of 71739 are 3, 2657. Prime factorization of 71739 in exponential form is:

71739 = 3³ × 2657¹

Step-2: Prime Factorization of 71757

Prime factors of 71757 are 3, 7, 17, 67. Prime factorization of 71757 in exponential form is:

71757 = 3² × 7¹ × 17¹ × 67¹

Step-3: Factors of 71739

List of positive integer factors of 71739 that divides 71739 without a remainder.

1, 3, 9, 27, 2657, 7971, 23913

Step-4: Factors of 71757

List of positive integer factors of 71757 that divides 71739 without a remainder.

1, 3, 7, 9, 17, 21, 51, 63, 67, 119, 153, 201, 357, 469, 603, 1071, 1139, 1407, 3417, 4221, 7973, 10251, 23919

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71739 and 71757. The biggest common factor number is the GCF number.
So the greatest common factor 71739 and 71757 is 9.

Also check out the Least Common Multiple of 71739 and 71757