What is the Greatest Common Factor of 87971 and 87984?

Greatest common factor (GCF) of 87971 and 87984 is 13.

GCF(87971,87984) = 13

We will now calculate the prime factors of 87971 and 87984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 87971 and 87984.

How to find the GCF of 87971 and 87984?

We will first find the prime factorization of 87971 and 87984. After we will calculate the factors of 87971 and 87984 and find the biggest common factor number .

Step-1: Prime Factorization of 87971

Prime factors of 87971 are 13, 67, 101. Prime factorization of 87971 in exponential form is:

87971 = 13¹ × 67¹ × 101¹

Step-2: Prime Factorization of 87984

Prime factors of 87984 are 2, 3, 13, 47. Prime factorization of 87984 in exponential form is:

87984 = 2⁴ × 3² × 13¹ × 47¹

Step-3: Factors of 87971

List of positive integer factors of 87971 that divides 87971 without a remainder.

1, 13, 67, 101, 871, 1313, 6767

Step-4: Factors of 87984

List of positive integer factors of 87984 that divides 87971 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 36, 39, 47, 48, 52, 72, 78, 94, 104, 117, 141, 144, 156, 188, 208, 234, 282, 312, 376, 423, 468, 564, 611, 624, 752, 846, 936, 1128, 1222, 1692, 1833, 1872, 2256, 2444, 3384, 3666, 4888, 5499, 6768, 7332, 9776, 10998, 14664, 21996, 29328, 43992

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 87971 and 87984. The biggest common factor number is the GCF number.
So the greatest common factor 87971 and 87984 is 13.

Also check out the Least Common Multiple of 87971 and 87984