Factorial

Number Theory Level 2

Find the last 5 digits of 125 ! 125! .


Notation: ! ! is the factorial notation. For example, 8 ! = 1 × 2 × 3 × ⋯ × 8 8! = 1\times2\times3\times\cdots\times8 .


The answer is 0.

Tasneem Khaled by Tasneem Khaled , 26, Bangladesh

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2 solutions

125 ! = 125! = 

1
 
188267717688892609974376770249160085759540364871492425887598231508353156331613598866882932889495923133646405445930057740630161919341380597818883457558547055524326375565007131770880000000000000000000000000000000

you do realise that we do have computers?

2 Helpful 0 Interesting 1 Brilliant 0 Confused

haha, that's the accurate way of doing it :D

Shubham Vermani - 3 years, 10 months ago

I like how you explained each step vividly! +1

I computed 124! by hand but I couldn't for the life of me figure out how to compute 125!.

Pi Han Goh - 3 years, 10 months ago

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Oh it's very simple, just multiply 124! by 5, 3 times.

Agnishom Chattopadhyay - 3 years, 10 months ago

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I don't know man. Multiplying a large number by 5 for 3 times? I'm not doing that. I prefer to compute 126! by hand. But no way am I computing 125! by hand.

Pi Han Goh - 3 years, 10 months ago

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@Pi Han Goh – You could hire some people to do it for you.

Agnishom Chattopadhyay - 3 years, 10 months ago

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@Agnishom Chattopadhyay – Good idea. In the meantime, let me start a kickstarter so that everyone can verify that the value of 125! that you've posted.

Pi Han Goh - 3 years, 10 months ago

I wanted you guys to solve it without the help of any computer @Agnishom Chattopadhyay

Tasneem Khaled - 3 years, 10 months ago

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Why? Computers are awesome. Aren't they?

Just kidding. I understand your point. I wanted to show that this problem is not as impossible as it sounds.

Agnishom Chattopadhyay - 3 years, 10 months ago

@Agnishom Chattopadhyay I know what you mean. As a matter of fact, programming and math are my true love :p

Tasneem Khaled - 3 years, 10 months ago
Tasneem Khaled
Jul 17, 2017

We know that whenever there is a five factorial, the last digit is going to be 0. Since there are lots of 5 factorials that make up a 125!, the last 5 digits are going to be 0 as well.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

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