What is the Greatest Common Factor of 35760 and 35769?

Greatest common factor (GCF) of 35760 and 35769 is 3.

GCF(35760,35769) = 3

We will now calculate the prime factors of 35760 and 35769, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35760 and 35769.

How to find the GCF of 35760 and 35769?

We will first find the prime factorization of 35760 and 35769. After we will calculate the factors of 35760 and 35769 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 35769

Prime factors of 35769 are 3, 11923. Prime factorization of 35769 in exponential form is:

35769 = 3¹ × 11923¹

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 35769

List of positive integer factors of 35769 that divides 35760 without a remainder.

1, 3, 11923

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35760 and 35769. The biggest common factor number is the GCF number.
So the greatest common factor 35760 and 35769 is 3.

Also check out the Least Common Multiple of 35760 and 35769