What is the Greatest Common Factor of 65100 and 65116?

Greatest common factor (GCF) of 65100 and 65116 is 4.

GCF(65100,65116) = 4

We will now calculate the prime factors of 65100 and 65116, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65100 and 65116.

How to find the GCF of 65100 and 65116?

We will first find the prime factorization of 65100 and 65116. After we will calculate the factors of 65100 and 65116 and find the biggest common factor number .

Step-1: Prime Factorization of 65100

Prime factors of 65100 are 2, 3, 5, 7, 31. Prime factorization of 65100 in exponential form is:

65100 = 2² × 3¹ × 5² × 7¹ × 31¹

Step-2: Prime Factorization of 65116

Prime factors of 65116 are 2, 73, 223. Prime factorization of 65116 in exponential form is:

65116 = 2² × 73¹ × 223¹

Step-3: Factors of 65100

List of positive integer factors of 65100 that divides 65100 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 31, 35, 42, 50, 60, 62, 70, 75, 84, 93, 100, 105, 124, 140, 150, 155, 175, 186, 210, 217, 300, 310, 350, 372, 420, 434, 465, 525, 620, 651, 700, 775, 868, 930, 1050, 1085, 1302, 1550, 1860, 2100, 2170, 2325, 2604, 3100, 3255, 4340, 4650, 5425, 6510, 9300, 10850, 13020, 16275, 21700, 32550

Step-4: Factors of 65116

List of positive integer factors of 65116 that divides 65100 without a remainder.

1, 2, 4, 73, 146, 223, 292, 446, 892, 16279, 32558

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65100 and 65116. The biggest common factor number is the GCF number.
So the greatest common factor 65100 and 65116 is 4.

Also check out the Least Common Multiple of 65100 and 65116