## Enter Multifactorial

Calculate the multifactorial 16!

^{3}We have 3 exclamation symbols (!)

Start at 16

Iterate backwards in steps of 3

Stop when we hit 1 or below

## Term 1

For term 1, we start with 16

## Term 2

Subtract 1 x 3 = 3 to get n(n - 3)

(n - 3) → 16 - 3 = 13

Our factorial term is:

16(13)

## Term 3

Subtract 2 x 3 = 6 to get n(n - 3)(n - 6)

(n - 6) → 16 - 6 = 10

Our factorial term is:

16(13)(10)

## Term 4

Subtract 3 x 3 = 9 to get n(n - 3)(n - 6)(n - 9)

(n - 9) → 16 - 9 = 7

Our factorial term is:

16(13)(10)(7)

## Term 5

Subtract 4 x 3 = 12 to get n(n - 3)(n - 6)(n - 9)(n - 12)

(n - 12) → 16 - 12 = 4

Our factorial term is:

16(13)(10)(7)(4)

## Term 6

Subtract 5 x 3 = 15 to get n(n - 3)(n - 6)(n - 9)(n - 12)(n - 15)

(n - 15) → 16 - 15 = 1

Our factorial term is:

16(13)(10)(7)(4)(1)

## Build final multifactorial answer:

16!

^{3} = n(n - 3)(n - 6)(n - 9)(n - 12)(n - 15)...

16!

^{3} = 16(13)(10)(7)(4)(1)

16!^{3} = **58,240**

### How does the Multifactorials Calculator work?

Calculates the multifactorial n!^{(m)}

This calculator has 1 input.

### What 1 formula is used for the Multifactorials Calculator?

- n!
^{(m)} = (n - m) * (n - m - m) * ... * 1

For more math formulas, check out our

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### What 3 concepts are covered in the Multifactorials Calculator?

- factorial
- The product of an integer and all the integers below it
- multifactorial
- generalisation of a factorial in which each element to be multiplied differs from the next by an integer
- permutation
- a way in which a set or number of things can be ordered or arranged.

_{n}P_{r} = n!/(n - r)!

### Example calculations for the Multifactorials Calculator

## Multifactorials Calculator Video

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