Join FunTrivia for Free: Hourly trivia games, quizzes, community, and more!
Fun Trivia
Ask FunTrivia: Questions and Answers
Answers to 100,000 Fascinating Questions
Welcome to FunTrivia's Question & Answer forum!

Search All Questions


Please cite any factual claims with citation links or references from authoritative sources. Editors continuously recheck submissions and claims.

Archived Questions

Goto Qn #


What is the largest 4-digit number that can be evenly divided by every single digit integer?

Question #113225. Asked by gc4evr.

Bronxiteone
Answer has 4 votes
Currently Best Answer
Bronxiteone
15 year member
61 replies

Answer has 4 votes.

Currently voted the best answer.
1*5*7*8*9=2520 which is the smallest 4 digit number satisfying the requirements.

2520*3=7560 , the largest number satisfying the requirements.

Mar 05 2010, 8:19 AM
avatar
Juggernaut314 star
Answer has 4 votes
Juggernaut314 star
15 year member
98 replies avatar

Answer has 4 votes.
This is a trick question. Zero is a single digit integer, and since you cannot divide by zero there is no 4 digit number satisfying this constraint.

From link https://en.wikipedia.org/wiki/Division_by_zero:

"In mathematics, a division is called a division by zero if the divisor is zero. Such a division can be formally expressed as a / 0 where a is the dividend. Whether this expression can be assigned a well-defined value depends upon the mathematical setting. In ordinary (real number) arithmetic, the expression has no meaning."

Mar 05 2010, 10:06 AM
avatar
Juggernaut314 star
Answer has 3 votes
Juggernaut314 star
15 year member
98 replies avatar

Answer has 3 votes.
It's worth noting that Bronxiteone's answer is correct if you say "every POSITIVE single digit integer".

I would additionally qualify that 2520 is the smallest number (4 digit or not) satisfying that requirement. To understand where 1*5*7*8*9 came from, list the numbers from 1 - 9 by their prime factorizations:

1 * 2 * 3 * (2^2) * 5 * (2*3) * 7 * (2^3) * (3^2)

Pick the least number of factors needed to express every number:

Using 3^2 gets 9 & 3
Using 2^3 gets 2, 4, & 8, and using a 3 from 3^2 gets us 8
Using 5 & 7 gets us 5 & 7
Using 1 gets us 1

That's all of them, and it multiplies out to 2520. To find the largest 4 digit number that can be evenly divided by every POSITIVE single digit integer is the same as finding the largest multiple of 2520 that is 4 digits. This is done by multiplying it by 3 to get 7560.

Mar 05 2010, 10:24 AM
gc4evr
Answer has 4 votes
gc4evr

Answer has 4 votes.
Thanks all. THe answer by Bronxiteone was what I was looking for, but Juggernaut314 was correct by pointing out the flaw of my stated question.
Thanks to you both.

Mar 06 2010, 7:02 AM
Bronxiteone
Answer has 3 votes
Bronxiteone
15 year member
61 replies

Answer has 3 votes.
Eleven is the smallest number NOT divisible by any one digit positive number except one.

Mar 06 2010, 4:02 PM
free email trivia FREE! Get a new mixed Fun Trivia quiz each day in your email. It's a fun way to start your day!


arrow Your Email Address:

Sign in or Create Free User ID to participate in the discussion