What is the Greatest Common Factor of 29738 and 29754?

Greatest common factor (GCF) of 29738 and 29754 is 2.

GCF(29738,29754) = 2

We will now calculate the prime factors of 29738 and 29754, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29738 and 29754.

How to find the GCF of 29738 and 29754?

We will first find the prime factorization of 29738 and 29754. After we will calculate the factors of 29738 and 29754 and find the biggest common factor number .

Step-1: Prime Factorization of 29738

Prime factors of 29738 are 2, 14869. Prime factorization of 29738 in exponential form is:

29738 = 2¹ × 14869¹

Step-2: Prime Factorization of 29754

Prime factors of 29754 are 2, 3, 19, 29. Prime factorization of 29754 in exponential form is:

29754 = 2¹ × 3³ × 19¹ × 29¹

Step-3: Factors of 29738

List of positive integer factors of 29738 that divides 29738 without a remainder.

1, 2, 14869

Step-4: Factors of 29754

List of positive integer factors of 29754 that divides 29738 without a remainder.

1, 2, 3, 6, 9, 18, 19, 27, 29, 38, 54, 57, 58, 87, 114, 171, 174, 261, 342, 513, 522, 551, 783, 1026, 1102, 1566, 1653, 3306, 4959, 9918, 14877

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29738 and 29754. The biggest common factor number is the GCF number.
So the greatest common factor 29738 and 29754 is 2.

Also check out the Least Common Multiple of 29738 and 29754