What is the Greatest Common Factor of 35365 and 35380?

Greatest common factor (GCF) of 35365 and 35380 is 5.

GCF(35365,35380) = 5

We will now calculate the prime factors of 35365 and 35380, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35365 and 35380.

How to find the GCF of 35365 and 35380?

We will first find the prime factorization of 35365 and 35380. After we will calculate the factors of 35365 and 35380 and find the biggest common factor number .

Step-1: Prime Factorization of 35365

Prime factors of 35365 are 5, 11, 643. Prime factorization of 35365 in exponential form is:

35365 = 5¹ × 11¹ × 643¹

Step-2: Prime Factorization of 35380

Prime factors of 35380 are 2, 5, 29, 61. Prime factorization of 35380 in exponential form is:

35380 = 2² × 5¹ × 29¹ × 61¹

Step-3: Factors of 35365

List of positive integer factors of 35365 that divides 35365 without a remainder.

1, 5, 11, 55, 643, 3215, 7073

Step-4: Factors of 35380

List of positive integer factors of 35380 that divides 35365 without a remainder.

1, 2, 4, 5, 10, 20, 29, 58, 61, 116, 122, 145, 244, 290, 305, 580, 610, 1220, 1769, 3538, 7076, 8845, 17690

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35365 and 35380. The biggest common factor number is the GCF number.
So the greatest common factor 35365 and 35380 is 5.

Also check out the Least Common Multiple of 35365 and 35380