What is the Greatest Common Factor of 35760 and 35770?

Greatest common factor (GCF) of 35760 and 35770 is 10.

GCF(35760,35770) = 10

We will now calculate the prime factors of 35760 and 35770, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35760 and 35770.

How to find the GCF of 35760 and 35770?

We will first find the prime factorization of 35760 and 35770. After we will calculate the factors of 35760 and 35770 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 35770

Prime factors of 35770 are 2, 5, 7, 73. Prime factorization of 35770 in exponential form is:

35770 = 2¹ × 5¹ × 7² × 73¹

Step-3: Factors of 35760

List of positive integer factors of 35760 that divides 35760 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

Step-4: Factors of 35770

List of positive integer factors of 35770 that divides 35760 without a remainder.

1, 2, 5, 7, 10, 14, 35, 49, 70, 73, 98, 146, 245, 365, 490, 511, 730, 1022, 2555, 3577, 5110, 7154, 17885

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35760 and 35770. The biggest common factor number is the GCF number.
So the greatest common factor 35760 and 35770 is 10.

Also check out the Least Common Multiple of 35760 and 35770