What is the Greatest Common Factor of 39996 and 40014?

Greatest common factor (GCF) of 39996 and 40014 is 18.

GCF(39996,40014) = 18

We will now calculate the prime factors of 39996 and 40014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39996 and 40014.

How to find the GCF of 39996 and 40014?

We will first find the prime factorization of 39996 and 40014. After we will calculate the factors of 39996 and 40014 and find the biggest common factor number .

Step-1: Prime Factorization of 39996

Prime factors of 39996 are 2, 3, 11, 101. Prime factorization of 39996 in exponential form is:

39996 = 2² × 3² × 11¹ × 101¹

Step-2: Prime Factorization of 40014

Prime factors of 40014 are 2, 3, 13, 19. Prime factorization of 40014 in exponential form is:

40014 = 2¹ × 3⁴ × 13¹ × 19¹

Step-3: Factors of 39996

List of positive integer factors of 39996 that divides 39996 without a remainder.

1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 101, 132, 198, 202, 303, 396, 404, 606, 909, 1111, 1212, 1818, 2222, 3333, 3636, 4444, 6666, 9999, 13332, 19998

Step-4: Factors of 40014

List of positive integer factors of 40014 that divides 39996 without a remainder.

1, 2, 3, 6, 9, 13, 18, 19, 26, 27, 38, 39, 54, 57, 78, 81, 114, 117, 162, 171, 234, 247, 342, 351, 494, 513, 702, 741, 1026, 1053, 1482, 1539, 2106, 2223, 3078, 4446, 6669, 13338, 20007

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39996 and 40014. The biggest common factor number is the GCF number.
So the greatest common factor 39996 and 40014 is 18.

Also check out the Least Common Multiple of 39996 and 40014