What is the Greatest Common Factor of 13748 and 13762?

Greatest common factor (GCF) of 13748 and 13762 is 14.

GCF(13748,13762) = 14

We will now calculate the prime factors of 13748 and 13762, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13748 and 13762.

How to find the GCF of 13748 and 13762?

We will first find the prime factorization of 13748 and 13762. After we will calculate the factors of 13748 and 13762 and find the biggest common factor number .

Step-1: Prime Factorization of 13748

Prime factors of 13748 are 2, 7, 491. Prime factorization of 13748 in exponential form is:

13748 = 2² × 7¹ × 491¹

Step-2: Prime Factorization of 13762

Prime factors of 13762 are 2, 7, 983. Prime factorization of 13762 in exponential form is:

13762 = 2¹ × 7¹ × 983¹

Step-3: Factors of 13748

List of positive integer factors of 13748 that divides 13748 without a remainder.

1, 2, 4, 7, 14, 28, 491, 982, 1964, 3437, 6874

Step-4: Factors of 13762

List of positive integer factors of 13762 that divides 13748 without a remainder.

1, 2, 7, 14, 983, 1966, 6881

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13748 and 13762. The biggest common factor number is the GCF number.
So the greatest common factor 13748 and 13762 is 14.

Also check out the Least Common Multiple of 13748 and 13762