What is the Greatest Common Factor of 19700 and 19710?

Greatest common factor (GCF) of 19700 and 19710 is 10.

GCF(19700,19710) = 10

We will now calculate the prime factors of 19700 and 19710, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19700 and 19710.

How to find the GCF of 19700 and 19710?

We will first find the prime factorization of 19700 and 19710. After we will calculate the factors of 19700 and 19710 and find the biggest common factor number .

Step-1: Prime Factorization of 19700

Prime factors of 19700 are 2, 5, 197. Prime factorization of 19700 in exponential form is:

19700 = 2² × 5² × 197¹

Step-2: Prime Factorization of 19710

Prime factors of 19710 are 2, 3, 5, 73. Prime factorization of 19710 in exponential form is:

19710 = 2¹ × 3³ × 5¹ × 73¹

Step-3: Factors of 19700

List of positive integer factors of 19700 that divides 19700 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 197, 394, 788, 985, 1970, 3940, 4925, 9850

Step-4: Factors of 19710

List of positive integer factors of 19710 that divides 19700 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 73, 90, 135, 146, 219, 270, 365, 438, 657, 730, 1095, 1314, 1971, 2190, 3285, 3942, 6570, 9855

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19700 and 19710. The biggest common factor number is the GCF number.
So the greatest common factor 19700 and 19710 is 10.

Also check out the Least Common Multiple of 19700 and 19710