What is the Greatest Common Factor of 29854 and 29874?

Greatest common factor (GCF) of 29854 and 29874 is 2.

GCF(29854,29874) = 2

We will now calculate the prime factors of 29854 and 29874, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29854 and 29874.

How to find the GCF of 29854 and 29874?

We will first find the prime factorization of 29854 and 29874. After we will calculate the factors of 29854 and 29874 and find the biggest common factor number .

Step-1: Prime Factorization of 29854

Prime factors of 29854 are 2, 11, 23, 59. Prime factorization of 29854 in exponential form is:

29854 = 2¹ × 11¹ × 23¹ × 59¹

Step-2: Prime Factorization of 29874

Prime factors of 29874 are 2, 3, 13, 383. Prime factorization of 29874 in exponential form is:

29874 = 2¹ × 3¹ × 13¹ × 383¹

Step-3: Factors of 29854

List of positive integer factors of 29854 that divides 29854 without a remainder.

1, 2, 11, 22, 23, 46, 59, 118, 253, 506, 649, 1298, 1357, 2714, 14927

Step-4: Factors of 29874

List of positive integer factors of 29874 that divides 29854 without a remainder.

1, 2, 3, 6, 13, 26, 39, 78, 383, 766, 1149, 2298, 4979, 9958, 14937

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29854 and 29874. The biggest common factor number is the GCF number.
So the greatest common factor 29854 and 29874 is 2.

Also check out the Least Common Multiple of 29854 and 29874