Factoring and Multiples
Prime Numbers

What are the factors and prime factors of 5040?

Answer

Wiki User
03/16/2009

5040 is a composite number because it has factors other than 1 and itself. It is not a prime number.

7! (also known as 7 factorial) = 1 x 2 x 3 x 4 x 5 x 6 x 7 = 5040.

The 60 factors of 5040 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 105, 112, 120, 126, 140, 144, 168, 180, 210, 240, 252, 280, 315, 336, 360, 420, 504, 560, 630, 720, 840, 1008, 1260, 1680, 2520, and 5040.

The factor pairs of 5040 are 1 x 5040, 2 x 2520, 3 x 1680, 4 x 1260, 5 x 1008, 6 x 840, 7 x 720, 8 x 630, 9 x 560, 10 x 504, 12 x 420, 14 x 360, 15 x 336, 16 x 315, 18 x 280, 20 x 252, 21 x 240, 24 x 210, 28 x 180, 30 x 168, 35 x 144, 36 x 140, 40 x 126, 42 x 120, 45 x 112, 48 x 104, 56 x 90, 60 x 84, 63 x 80, and 70 x 72.

The proper factors of 5040 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 105, 112, 120, 126, 140, 144, 168, 180, 210, 240, 252, 280, 315, 336, 360, 420, 504, 560, 630, 720, 840, 1008, 1260, 1680, and 2520 or,

if the definition you are using excludes 1, they are 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 105, 112, 120, 126, 140, 144, 168, 180, 210, 240, 252, 280, 315, 336, 360, 420, 504, 560, 630, 720, 840, 1008, 1260, 1680, and 2520.

The prime factors of 5040 are 2, 2, 2, 2, 3, 3, 5, and 7. Note: There is repetition of these factors, so if the prime factors are being listed instead of the prime factorization, usually only the distinct prime factors are listed.

The distinct prime factors (listing each prime factor only once) or 5040 are 2, 3, 5, and 7.

The prime factorization of 5040 are 2 x 2 x 2 x 2 x 3 x 3 x 5 x 7 or, in exponential form, 24 x 32 x 5 x 7.

NOTE: There cannot be common factors, a greatest common factor, or a least common multiple because "common" refers to factors or multiples that two or more numbers have in common.