What is the Greatest Common Factor of 14640 and 14658?

Greatest common factor (GCF) of 14640 and 14658 is 6.

GCF(14640,14658) = 6

We will now calculate the prime factors of 14640 and 14658, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14640 and 14658.

How to find the GCF of 14640 and 14658?

We will first find the prime factorization of 14640 and 14658. After we will calculate the factors of 14640 and 14658 and find the biggest common factor number .

Step-1: Prime Factorization of 14640

Prime factors of 14640 are 2, 3, 5, 61. Prime factorization of 14640 in exponential form is:

14640 = 2⁴ × 3¹ × 5¹ × 61¹

Step-2: Prime Factorization of 14658

Prime factors of 14658 are 2, 3, 7, 349. Prime factorization of 14658 in exponential form is:

14658 = 2¹ × 3¹ × 7¹ × 349¹

Step-3: Factors of 14640

List of positive integer factors of 14640 that divides 14640 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 61, 80, 120, 122, 183, 240, 244, 305, 366, 488, 610, 732, 915, 976, 1220, 1464, 1830, 2440, 2928, 3660, 4880, 7320

Step-4: Factors of 14658

List of positive integer factors of 14658 that divides 14640 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 349, 698, 1047, 2094, 2443, 4886, 7329

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14640 and 14658. The biggest common factor number is the GCF number.
So the greatest common factor 14640 and 14658 is 6.

Also check out the Least Common Multiple of 14640 and 14658