What is the Greatest Common Factor of 33698 and 33712?

Greatest common factor (GCF) of 33698 and 33712 is 14.

GCF(33698,33712) = 14

We will now calculate the prime factors of 33698 and 33712, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 33698 and 33712.

How to find the GCF of 33698 and 33712?

We will first find the prime factorization of 33698 and 33712. After we will calculate the factors of 33698 and 33712 and find the biggest common factor number .

Step-1: Prime Factorization of 33698

Prime factors of 33698 are 2, 7, 29, 83. Prime factorization of 33698 in exponential form is:

33698 = 2¹ × 7¹ × 29¹ × 83¹

Step-2: Prime Factorization of 33712

Prime factors of 33712 are 2, 7, 43. Prime factorization of 33712 in exponential form is:

33712 = 2⁴ × 7² × 43¹

Step-3: Factors of 33698

List of positive integer factors of 33698 that divides 33698 without a remainder.

1, 2, 7, 14, 29, 58, 83, 166, 203, 406, 581, 1162, 2407, 4814, 16849

Step-4: Factors of 33712

List of positive integer factors of 33712 that divides 33698 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 43, 49, 56, 86, 98, 112, 172, 196, 301, 344, 392, 602, 688, 784, 1204, 2107, 2408, 4214, 4816, 8428, 16856

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 33698 and 33712. The biggest common factor number is the GCF number.
So the greatest common factor 33698 and 33712 is 14.

Also check out the Least Common Multiple of 33698 and 33712