The Prime Party Trick

User Rating:  / 0
PoorBest 

What is a prime number?

A number that only has 2 factors, itself and one. A factor of a number is a number that divides into it fully. 

10 has factors of 1, 2, 5, and 10

24 has factors 1, 2, 3, 4, 6, 8, 12, and 24

But 7 has factors 1 and 7....it is a prime number

1 only has one factor, itself, 1. It is not a prime, it doesn't fit the criteria.

 

Here is a list of the first natural prime numbers:

2,3,5,7,11,13,17,19,23,29,31...……..

 

The trick

Think of a 3 digit number. Use a calculator to multiply itself by 7, 11, and 13

If you chose 264, you would type 264 x 7 x 11 x 13 and then =

Surprising to say, the answer in this case is 264264. Try some more. It's simply just a repeat of itself. 

Now you can bet your friends and family that you can work out the answer in your head and write it down quicker than they can using a calculator. 

 

Why does it work?

7 x 11 x 13 = 1001. What's happening is the decimal place is moved along by 3 when you multiply by 1000, making 3 vacant place value digits. i.e. 264 x 1000 = 264000

 

The extra 1 in 1001 means that the original 3 digit number is being added into these vacant columns. i.e. 264264

 

Does it work for 2 or 4 digit numbers?

Yes, but it needs a little tweaking. 2 digit numbers end up with a 0 in between

76 x 7 x 11 x13 = 76076

4 digit numbers end up with a bit of mental addition that might spoil your party mood! You need to add the last digit of the first number to the fist digit of the last number. i.e. for 1784

 

1 7 8 4

        1 7 8 4 +


1 7 8 5 7 8 4

If you can figure it out, you can ramp up the odds each time, and impress a few people.