Are numbers divisible by 9 also divisible by 3?

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Solution

Yes every number divisible by 9 will be divisible by 3. But it is not necessary that every number that is divisible by 3 is divisible by 9.

For example: 81 is divisible by 3 and 9 but 24 is divisible by 3, not divisible by 9.

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2, 3, 5, 9

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Which of the following statements are true?

(a) If a number is divisible by 3, it must be divisible by 9.

(b) If a number is divisible by 9, it must be divisible by 3.

(d) If a number is divisible by 9 and 10 both, then it must be divisible by 90.

(e) If two numbers are co-primes, at least one of them must be prime.

(f) All numbers which are divisible by 4 must also be divisible by 8.

(g) All numbers which are divisible by 8 must also be divisible by 4.

(h) If a number exactly divides two numbers separately, it must exactly divide their sum.

(i) If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately.

(i) All numbers divisible by 3 must also be divisible by 6

(ii) All numbers divisible by 6 must also be divisible by 3

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