What is the Greatest Common Factor of 30736 and 30742?

Greatest common factor (GCF) of 30736 and 30742 is 2.

GCF(30736,30742) = 2

We will now calculate the prime factors of 30736 and 30742, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30736 and 30742.

How to find the GCF of 30736 and 30742?

We will first find the prime factorization of 30736 and 30742. After we will calculate the factors of 30736 and 30742 and find the biggest common factor number .

Step-1: Prime Factorization of 30736

Prime factors of 30736 are 2, 17, 113. Prime factorization of 30736 in exponential form is:

30736 = 2⁴ × 17¹ × 113¹

Step-2: Prime Factorization of 30742

Prime factors of 30742 are 2, 19, 809. Prime factorization of 30742 in exponential form is:

30742 = 2¹ × 19¹ × 809¹

Step-3: Factors of 30736

List of positive integer factors of 30736 that divides 30736 without a remainder.

1, 2, 4, 8, 16, 17, 34, 68, 113, 136, 226, 272, 452, 904, 1808, 1921, 3842, 7684, 15368

Step-4: Factors of 30742

List of positive integer factors of 30742 that divides 30736 without a remainder.

1, 2, 19, 38, 809, 1618, 15371

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30736 and 30742. The biggest common factor number is the GCF number.
So the greatest common factor 30736 and 30742 is 2.

Also check out the Least Common Multiple of 30736 and 30742