How can you quickly check whether a number is exactly divisible by 9?

According to mathematicsnotebook:

A number is divisible by 9 if the sum of its digits is divisible by 9. For large numbers this rule can be applied again to the result. In addition, the final iteration will result in a 9.

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47 Comments

Louella Wilson

I've always thought it a useless fact. Interesting, but useless. I can divide by 9 as quickly, or quicker, than adding digits before dividing that sum by 9.

Georgina Morrison

SUM is the answer to an addition question and PRODUCT is the answer to a multiplication questionHenry Ford 1889,

Henry Ford 1889

When I was at school, sum and product were one and the same.

Chris Brown

Or if the separate digits add up to 9. 9x2=18; 9x3=27 etc. Also, for any number added to 9, the digits add up to the number added on: 9+1=10; 9+8=17...

LevibatteryCSA (Dave)

I don't use Math any more.

Brian Reynolds

I recently watched a TV program called "The human calculator". The man was incredible. He would stop strangers in the street and after a few questions would tell them their birth dates. He then demonstrated all sorts of calculations with the number nine. In one scene he was in a supermarket and tallied a large customer bill in a matter of seconds. An amazing program and I hope there are more episodes to come.

Nikki Proctor

that is how i taught my girls their 9 x tables. everything adds up to nine (ie 4X9=36, 3+6=9)

jonbroberts

Same rule supplies with 3. If the sum of the digits is divisible by 3 then the number is also divisible by 3.

Richard Rubright

Actually, the sume of the digits must be exactly 9. If more than 1 digit keep adding until there is only the digit 9.

james parrillo

Joseph A. Robitaille, The question asked another way to tell if a number may be divided by 9 evenly. It is possible to add all the digits in the number and then tell if the sum of the digits is also divisible by 9. Dividing the original number by 9 and adding and dividing that number by 9 both work to tell if the number is evenly divisible by 9. Thank you, Christine, James' wife