Choose the correct statement from the given options.

If a number is divisible by 8, it will also be divisible by 32.

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If a number is divisible by 8, it will also be divisible by 3

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If a number is divisible by 8, it will also be divisible by 4.

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If a number is divisible by 8, it will also be divisible by 6.

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Solution

The correct option is C If a number is divisible by 8, it will also be divisible by 4.
If a number is divisible by a particular number, it is also divisible by all the factors of that particular number.

For example , 16 is divisible by 8.
and 16 is also divisible by 4 and 2.
This is because the factors of 8 = 1, 2, 4 and 8.
Hence 16 is divisible by all the factors of 8 as well.

$∴$ If a number is divisible by 8, it will also be divisible by 2 and 4.

However the opposite is not true. For example 40 is divisible by 8 but not by 32.

3 and 6 are not factors of 8, hence a number divisible by 8,need not be divisible by 3 or 6.

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Similar questions

Q. If a number is divisible by 8 then its last _____ digits will also be divisible by 8.

Choose the correct option regarding the accuracy of the given statements:
Statement 1: All numbers divisible by 4 must also be divisible by 8
Statement 2: All numbers divisible by 8 must also be divisible by 4

All numbers divisible by 4 must also be divisible by 8 and all numbers divisible by 8 must also be divisible by 4

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.

Question 1

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.
(c) If a number is divisible by 18, it must be divisible by both 3 and 6.
(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.

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