What is the Greatest Common Factor of 35740 and 35760?

Greatest common factor (GCF) of 35740 and 35760 is 20.

GCF(35740,35760) = 20

We will now calculate the prime factors of 35740 and 35760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35740 and 35760.

How to find the GCF of 35740 and 35760?

We will first find the prime factorization of 35740 and 35760. After we will calculate the factors of 35740 and 35760 and find the biggest common factor number .

Step-1: Prime Factorization of 35740

Prime factors of 35740 are 2, 5, 1787. Prime factorization of 35740 in exponential form is:

35740 = 2² × 5¹ × 1787¹

Step-2: Prime Factorization of 35760

Prime factors of 35760 are 2, 3, 5, 149. Prime factorization of 35760 in exponential form is:

35760 = 2⁴ × 3¹ × 5¹ × 149¹

Step-3: Factors of 35740

List of positive integer factors of 35740 that divides 35740 without a remainder.

1, 2, 4, 5, 10, 20, 1787, 3574, 7148, 8935, 17870

Step-4: Factors of 35760

List of positive integer factors of 35760 that divides 35740 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 149, 240, 298, 447, 596, 745, 894, 1192, 1490, 1788, 2235, 2384, 2980, 3576, 4470, 5960, 7152, 8940, 11920, 17880

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35740 and 35760. The biggest common factor number is the GCF number.
So the greatest common factor 35740 and 35760 is 20.

Also check out the Least Common Multiple of 35740 and 35760