What is the Greatest Common Factor of 39858 and 39872?

Greatest common factor (GCF) of 39858 and 39872 is 14.

GCF(39858,39872) = 14

We will now calculate the prime factors of 39858 and 39872, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39858 and 39872.

How to find the GCF of 39858 and 39872?

We will first find the prime factorization of 39858 and 39872. After we will calculate the factors of 39858 and 39872 and find the biggest common factor number .

Step-1: Prime Factorization of 39858

Prime factors of 39858 are 2, 3, 7, 13, 73. Prime factorization of 39858 in exponential form is:

39858 = 2¹ × 3¹ × 7¹ × 13¹ × 73¹

Step-2: Prime Factorization of 39872

Prime factors of 39872 are 2, 7, 89. Prime factorization of 39872 in exponential form is:

39872 = 2⁶ × 7¹ × 89¹

Step-3: Factors of 39858

List of positive integer factors of 39858 that divides 39858 without a remainder.

1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 73, 78, 91, 146, 182, 219, 273, 438, 511, 546, 949, 1022, 1533, 1898, 2847, 3066, 5694, 6643, 13286, 19929

Step-4: Factors of 39872

List of positive integer factors of 39872 that divides 39858 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 89, 112, 178, 224, 356, 448, 623, 712, 1246, 1424, 2492, 2848, 4984, 5696, 9968, 19936

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39858 and 39872. The biggest common factor number is the GCF number.
So the greatest common factor 39858 and 39872 is 14.

Also check out the Least Common Multiple of 39858 and 39872