What is the Greatest Common Factor of 19775 and 19785?

Greatest common factor (GCF) of 19775 and 19785 is 5.

GCF(19775,19785) = 5

We will now calculate the prime factors of 19775 and 19785, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19775 and 19785.

How to find the GCF of 19775 and 19785?

We will first find the prime factorization of 19775 and 19785. After we will calculate the factors of 19775 and 19785 and find the biggest common factor number .

Step-1: Prime Factorization of 19775

Prime factors of 19775 are 5, 7, 113. Prime factorization of 19775 in exponential form is:

19775 = 5² × 7¹ × 113¹

Step-2: Prime Factorization of 19785

Prime factors of 19785 are 3, 5, 1319. Prime factorization of 19785 in exponential form is:

19785 = 3¹ × 5¹ × 1319¹

Step-3: Factors of 19775

List of positive integer factors of 19775 that divides 19775 without a remainder.

1, 5, 7, 25, 35, 113, 175, 565, 791, 2825, 3955

Step-4: Factors of 19785

List of positive integer factors of 19785 that divides 19775 without a remainder.

1, 3, 5, 15, 1319, 3957, 6595

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19775 and 19785. The biggest common factor number is the GCF number.
So the greatest common factor 19775 and 19785 is 5.

Also check out the Least Common Multiple of 19775 and 19785