###### Asked in 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.