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There are **14** NRICH Mathematical resources connected to **Factorials**, you may find related items under Properties of numbers.

Problem
Primary curriculum
Secondary curriculum
### Fac-finding

Lyndon chose this as one of his favourite problems. It is accessible but needs some careful analysis of what is included and what is not. A systematic approach is really helpful.

Age 14 to 16

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Binomial Coefficients

An introduction to the binomial coefficient, and exploration of some of the formulae it satisfies.

Age 14 to 18

Problem
Primary curriculum
Secondary curriculum
### Seriesly

Prove that k.k! = (k+1)! - k! and sum the series 1.1! + 2.2! + 3.3! +...+n.n!

Age 16 to 18

ShortChallenge Level

Problem
Primary curriculum
Secondary curriculum
### How Does Your Function Grow?

Compares the size of functions f(n) for large values of n.

Age 16 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### The Harmonic Triangle and Pascal's Triangle

The harmonic triangle is built from fractions with unit numerators using a rule very similar to Pascal's triangle.

Age 16 to 18

Problem
Primary curriculum
Secondary curriculum
### Powerful Factorial

6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest power of two that divides exactly into 100!?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Factoring Factorials

Find the highest power of 11 that will divide into 1000! exactly.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Factorial

How many zeros are there at the end of the number which is the product of first hundred positive integers?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Forgotten Number

I have forgotten the number of the combination of the lock on my briefcase. I did have a method for remembering it...

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Seriesly

Prove that k.k! = (k+1)! - k! and sum the series 1.1! + 2.2! + 3.3! +...+n.n!

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Squaresearch

Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### N000ughty Thoughts

How many noughts are at the end of these giant numbers?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Growing

Which is larger: (a) 1.000001^{1000000} or 2? (b) 100^{300} or 300! (i.e.factorial 300)

Age 16 to 18

Challenge Level