What is the Greatest Common Factor of 31834 and 31840?

Greatest common factor (GCF) of 31834 and 31840 is 2.

GCF(31834,31840) = 2

We will now calculate the prime factors of 31834 and 31840, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31834 and 31840.

How to find the GCF of 31834 and 31840?

We will first find the prime factorization of 31834 and 31840. After we will calculate the factors of 31834 and 31840 and find the biggest common factor number .

Step-1: Prime Factorization of 31834

Prime factors of 31834 are 2, 11, 1447. Prime factorization of 31834 in exponential form is:

31834 = 2¹ × 11¹ × 1447¹

Step-2: Prime Factorization of 31840

Prime factors of 31840 are 2, 5, 199. Prime factorization of 31840 in exponential form is:

31840 = 2⁵ × 5¹ × 199¹

Step-3: Factors of 31834

List of positive integer factors of 31834 that divides 31834 without a remainder.

1, 2, 11, 22, 1447, 2894, 15917

Step-4: Factors of 31840

List of positive integer factors of 31840 that divides 31834 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160, 199, 398, 796, 995, 1592, 1990, 3184, 3980, 6368, 7960, 15920

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31834 and 31840. The biggest common factor number is the GCF number.
So the greatest common factor 31834 and 31840 is 2.

Also check out the Least Common Multiple of 31834 and 31840