What is the Greatest Common Factor of 87975 and 87984?

Greatest common factor (GCF) of 87975 and 87984 is 9.

GCF(87975,87984) = 9

We will now calculate the prime factors of 87975 and 87984, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 87975 and 87984.

How to find the GCF of 87975 and 87984?

We will first find the prime factorization of 87975 and 87984. After we will calculate the factors of 87975 and 87984 and find the biggest common factor number .

Step-1: Prime Factorization of 87975

Prime factors of 87975 are 3, 5, 17, 23. Prime factorization of 87975 in exponential form is:

87975 = 3² × 5² × 17¹ × 23¹

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 87975

List of positive integer factors of 87975 that divides 87975 without a remainder.

1, 3, 5, 9, 15, 17, 23, 25, 45, 51, 69, 75, 85, 115, 153, 207, 225, 255, 345, 391, 425, 575, 765, 1035, 1173, 1275, 1725, 1955, 3519, 3825, 5175, 5865, 9775, 17595, 29325

Step-4: Factors of 87984

List of positive integer factors of 87984 that divides 87975 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 87975 and 87984. The biggest common factor number is the GCF number.
So the greatest common factor 87975 and 87984 is 9.

Also check out the Least Common Multiple of 87975 and 87984