What is the Greatest Common Factor of 19750 and 19770?

Greatest common factor (GCF) of 19750 and 19770 is 10.

GCF(19750,19770) = 10

We will now calculate the prime factors of 19750 and 19770, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19750 and 19770.

How to find the GCF of 19750 and 19770?

We will first find the prime factorization of 19750 and 19770. After we will calculate the factors of 19750 and 19770 and find the biggest common factor number .

Step-1: Prime Factorization of 19750

Prime factors of 19750 are 2, 5, 79. Prime factorization of 19750 in exponential form is:

19750 = 2¹ × 5³ × 79¹

Step-2: Prime Factorization of 19770

Prime factors of 19770 are 2, 3, 5, 659. Prime factorization of 19770 in exponential form is:

19770 = 2¹ × 3¹ × 5¹ × 659¹

Step-3: Factors of 19750

List of positive integer factors of 19750 that divides 19750 without a remainder.

1, 2, 5, 10, 25, 50, 79, 125, 158, 250, 395, 790, 1975, 3950, 9875

Step-4: Factors of 19770

List of positive integer factors of 19770 that divides 19750 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 659, 1318, 1977, 3295, 3954, 6590, 9885

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19750 and 19770. The biggest common factor number is the GCF number.
So the greatest common factor 19750 and 19770 is 10.

Also check out the Least Common Multiple of 19750 and 19770