What is the Greatest Common Factor of 1700 and 1712?

Greatest common factor (GCF) of 1700 and 1712 is 4.

GCF(1700,1712) = 4

We will now calculate the prime factors of 1700 and 1712, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1700 and 1712.

How to find the GCF of 1700 and 1712?

We will first find the prime factorization of 1700 and 1712. After we will calculate the factors of 1700 and 1712 and find the biggest common factor number .

Step-1: Prime Factorization of 1700

Prime factors of 1700 are 2, 5, 17. Prime factorization of 1700 in exponential form is:

1700 = 2² × 5² × 17¹

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 1700

List of positive integer factors of 1700 that divides 1700 without a remainder.

1, 2, 4, 5, 10, 17, 20, 25, 34, 50, 68, 85, 100, 170, 340, 425, 850

Step-4: Factors of 1712

List of positive integer factors of 1712 that divides 1700 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 1700 and 1712. The biggest common factor number is the GCF number.
So the greatest common factor 1700 and 1712 is 4.

Also check out the Least Common Multiple of 1700 and 1712