What is the Greatest Common Factor of 17696 and 17700?

Greatest common factor (GCF) of 17696 and 17700 is 4.

GCF(17696,17700) = 4

We will now calculate the prime factors of 17696 and 17700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17696 and 17700.

How to find the GCF of 17696 and 17700?

We will first find the prime factorization of 17696 and 17700. After we will calculate the factors of 17696 and 17700 and find the biggest common factor number .

Step-1: Prime Factorization of 17696

Prime factors of 17696 are 2, 7, 79. Prime factorization of 17696 in exponential form is:

17696 = 2⁵ × 7¹ × 79¹

Step-2: Prime Factorization of 17700

Prime factors of 17700 are 2, 3, 5, 59. Prime factorization of 17700 in exponential form is:

17700 = 2² × 3¹ × 5² × 59¹

Step-3: Factors of 17696

List of positive integer factors of 17696 that divides 17696 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 79, 112, 158, 224, 316, 553, 632, 1106, 1264, 2212, 2528, 4424, 8848

Step-4: Factors of 17700

List of positive integer factors of 17700 that divides 17696 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 59, 60, 75, 100, 118, 150, 177, 236, 295, 300, 354, 590, 708, 885, 1180, 1475, 1770, 2950, 3540, 4425, 5900, 8850

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17696 and 17700. The biggest common factor number is the GCF number.
So the greatest common factor 17696 and 17700 is 4.

Also check out the Least Common Multiple of 17696 and 17700