What is the Greatest Common Factor of 11298 and 11312?

Greatest common factor (GCF) of 11298 and 11312 is 14.

GCF(11298,11312) = 14

We will now calculate the prime factors of 11298 and 11312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 11298 and 11312.

How to find the GCF of 11298 and 11312?

We will first find the prime factorization of 11298 and 11312. After we will calculate the factors of 11298 and 11312 and find the biggest common factor number .

Step-1: Prime Factorization of 11298

Prime factors of 11298 are 2, 3, 7, 269. Prime factorization of 11298 in exponential form is:

11298 = 2¹ × 3¹ × 7¹ × 269¹

Step-2: Prime Factorization of 11312

Prime factors of 11312 are 2, 7, 101. Prime factorization of 11312 in exponential form is:

11312 = 2⁴ × 7¹ × 101¹

Step-3: Factors of 11298

List of positive integer factors of 11298 that divides 11298 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 269, 538, 807, 1614, 1883, 3766, 5649

Step-4: Factors of 11312

List of positive integer factors of 11312 that divides 11298 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 101, 112, 202, 404, 707, 808, 1414, 1616, 2828, 5656

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 11298 and 11312. The biggest common factor number is the GCF number.
So the greatest common factor 11298 and 11312 is 14.

Also check out the Least Common Multiple of 11298 and 11312