No Math Needed!

Number Theory Level 2

I lied! There is a tiny bit of math involved - however, this problem is possible to solve mentally.

What are the last 3 digits of $123456789•987654321$ ?

Hint: You don't need to multiply the two numbers all the way.

1 solution

Hunter Edwards
Oct 31, 2017

If you are attempting to find the last 3 digits - only the last three digits of each factor are required.

So $789 • 321 =$

$1 • 789 = 789$ $20 • 789 = 15,780$ ( the 15,000 is irrelevant) $300 • 789 = 236,700$ ( the 236,000 is irrelevant)

So - add the following $789 + 780 + 700 = 2269$ - last three digits are $269$