What is the Greatest Common Factor of 1696 and 1712?

Greatest common factor (GCF) of 1696 and 1712 is 16.

GCF(1696,1712) = 16

We will now calculate the prime factors of 1696 and 1712, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1696 and 1712.

How to find the GCF of 1696 and 1712?

We will first find the prime factorization of 1696 and 1712. After we will calculate the factors of 1696 and 1712 and find the biggest common factor number .

Step-1: Prime Factorization of 1696

Prime factors of 1696 are 2, 53. Prime factorization of 1696 in exponential form is:

1696 = 2⁵ × 53¹

Step-2: Prime Factorization of 1712

Prime factors of 1712 are 2, 107. Prime factorization of 1712 in exponential form is:

1712 = 2⁴ × 107¹

Step-3: Factors of 1696

List of positive integer factors of 1696 that divides 1696 without a remainder.

1, 2, 4, 8, 16, 32, 53, 106, 212, 424, 848

Step-4: Factors of 1712

List of positive integer factors of 1712 that divides 1696 without a remainder.

1, 2, 4, 8, 16, 107, 214, 428, 856

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1696 and 1712. The biggest common factor number is the GCF number.
So the greatest common factor 1696 and 1712 is 16.

Also check out the Least Common Multiple of 1696 and 1712