What is the Greatest Common Factor of 31840 and 31854?

Greatest common factor (GCF) of 31840 and 31854 is 2.

GCF(31840,31854) = 2

We will now calculate the prime factors of 31840 and 31854, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31840 and 31854.

How to find the GCF of 31840 and 31854?

We will first find the prime factorization of 31840 and 31854. After we will calculate the factors of 31840 and 31854 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 31854

Prime factors of 31854 are 2, 3, 5309. Prime factorization of 31854 in exponential form is:

31854 = 2¹ × 3¹ × 5309¹

Step-3: Factors of 31840

List of positive integer factors of 31840 that divides 31840 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

Step-4: Factors of 31854

List of positive integer factors of 31854 that divides 31840 without a remainder.

1, 2, 3, 6, 5309, 10618, 15927

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31840 and 31854. The biggest common factor number is the GCF number.
So the greatest common factor 31840 and 31854 is 2.

Also check out the Least Common Multiple of 31840 and 31854