What is the Greatest Common Factor of 51709 and 51714?

Greatest common factor (GCF) of 51709 and 51714 is 1.

GCF(51709,51714) = 1

We will now calculate the prime factors of 51709 and 51714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51709 and 51714.

How to find the GCF of 51709 and 51714?

We will first find the prime factorization of 51709 and 51714. After we will calculate the factors of 51709 and 51714 and find the biggest common factor number .

Step-1: Prime Factorization of 51709

Prime factors of 51709 are 7, 83, 89. Prime factorization of 51709 in exponential form is:

51709 = 7¹ × 83¹ × 89¹

Step-2: Prime Factorization of 51714

Prime factors of 51714 are 2, 3, 13, 17. Prime factorization of 51714 in exponential form is:

51714 = 2¹ × 3² × 13² × 17¹

Step-3: Factors of 51709

List of positive integer factors of 51709 that divides 51709 without a remainder.

1, 7, 83, 89, 581, 623, 7387

Step-4: Factors of 51714

List of positive integer factors of 51714 that divides 51709 without a remainder.

1, 2, 3, 6, 9, 13, 17, 18, 26, 34, 39, 51, 78, 102, 117, 153, 169, 221, 234, 306, 338, 442, 507, 663, 1014, 1326, 1521, 1989, 2873, 3042, 3978, 5746, 8619, 17238, 25857

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51709 and 51714. The biggest common factor number is the GCF number.
So the greatest common factor 51709 and 51714 is 1.

Also check out the Least Common Multiple of 51709 and 51714