Do Not Use a Calculator: Divisibility By 9

Number Theory Level 1

Is 7073598799 7073598799 divisible by 9?

I Don't Nkow Can't Say Yes No

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Victor Paes Plinio by Victor Paes Plinio , 21, Brazil

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3 solutions

Aman Gautam
Oct 15, 2014

Numbers are divisible by 9 if the sum of all the individual digits is evenly divisible by 9.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Why? can you prove it @Aman Gautam

U Z - 6 years, 7 months ago

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Consider a 2 digit number 10a + b = 9a + (a+b).

We know that 9a is divisible by 9, so 10a + b will be divisible by 9 if and only if a+b is.

Similarly, 100a + 10b + c = 99a + 9b + (a + b + c), and 99a + 9b is divisible by 9, so the total will be divisible by 9 if and only if a + b + c is. hope you understood.....

Aman Gautam - 6 years, 7 months ago
Syed Hamza Khalid
May 11, 2017

Because the sum of the digits is 64 64 and 64 64 is not divisible by 9.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Vishal S
Dec 17, 2014

Since the sum of the digits of the number 7079598799 is not divisible 9

therefore the given number is not divisible 9

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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