What is the Greatest Common Factor of 14742 and 14749?

Greatest common factor (GCF) of 14742 and 14749 is 7.

GCF(14742,14749) = 7

We will now calculate the prime factors of 14742 and 14749, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14742 and 14749.

How to find the GCF of 14742 and 14749?

We will first find the prime factorization of 14742 and 14749. After we will calculate the factors of 14742 and 14749 and find the biggest common factor number .

Step-1: Prime Factorization of 14742

Prime factors of 14742 are 2, 3, 7, 13. Prime factorization of 14742 in exponential form is:

14742 = 2¹ × 3⁴ × 7¹ × 13¹

Step-2: Prime Factorization of 14749

Prime factors of 14749 are 7, 43. Prime factorization of 14749 in exponential form is:

14749 = 7³ × 43¹

Step-3: Factors of 14742

List of positive integer factors of 14742 that divides 14742 without a remainder.

1, 2, 3, 6, 7, 9, 13, 14, 18, 21, 26, 27, 39, 42, 54, 63, 78, 81, 91, 117, 126, 162, 182, 189, 234, 273, 351, 378, 546, 567, 702, 819, 1053, 1134, 1638, 2106, 2457, 4914, 7371

Step-4: Factors of 14749

List of positive integer factors of 14749 that divides 14742 without a remainder.

1, 7, 43, 49, 301, 343, 2107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14742 and 14749. The biggest common factor number is the GCF number.
So the greatest common factor 14742 and 14749 is 7.

Also check out the Least Common Multiple of 14742 and 14749