What is the Greatest Common Factor of 9100 and 9114?

Greatest common factor (GCF) of 9100 and 9114 is 14.

GCF(9100,9114) = 14

We will now calculate the prime factors of 9100 and 9114, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9100 and 9114.

How to find the GCF of 9100 and 9114?

We will first find the prime factorization of 9100 and 9114. After we will calculate the factors of 9100 and 9114 and find the biggest common factor number .

Step-1: Prime Factorization of 9100

Prime factors of 9100 are 2, 5, 7, 13. Prime factorization of 9100 in exponential form is:

9100 = 2² × 5² × 7¹ × 13¹

Step-2: Prime Factorization of 9114

Prime factors of 9114 are 2, 3, 7, 31. Prime factorization of 9114 in exponential form is:

9114 = 2¹ × 3¹ × 7² × 31¹

Step-3: Factors of 9100

List of positive integer factors of 9100 that divides 9100 without a remainder.

1, 2, 4, 5, 7, 10, 13, 14, 20, 25, 26, 28, 35, 50, 52, 65, 70, 91, 100, 130, 140, 175, 182, 260, 325, 350, 364, 455, 650, 700, 910, 1300, 1820, 2275, 4550

Step-4: Factors of 9114

List of positive integer factors of 9114 that divides 9100 without a remainder.

1, 2, 3, 6, 7, 14, 21, 31, 42, 49, 62, 93, 98, 147, 186, 217, 294, 434, 651, 1302, 1519, 3038, 4557

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9100 and 9114. The biggest common factor number is the GCF number.
So the greatest common factor 9100 and 9114 is 14.

Also check out the Least Common Multiple of 9100 and 9114