What is the Greatest Common Factor of 65100 and 65107?

Greatest common factor (GCF) of 65100 and 65107 is 7.

GCF(65100,65107) = 7

We will now calculate the prime factors of 65100 and 65107, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65100 and 65107.

How to find the GCF of 65100 and 65107?

We will first find the prime factorization of 65100 and 65107. After we will calculate the factors of 65100 and 65107 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 65107

Prime factors of 65107 are 7, 71, 131. Prime factorization of 65107 in exponential form is:

65107 = 7¹ × 71¹ × 131¹

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 65107

List of positive integer factors of 65107 that divides 65100 without a remainder.

1, 7, 71, 131, 497, 917, 9301

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65100 and 65107. The biggest common factor number is the GCF number.
So the greatest common factor 65100 and 65107 is 7.

Also check out the Least Common Multiple of 65100 and 65107