All numbers divisible by $4$ must also be divisible by $8 .$

True

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False

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Solution

The correct option is B False
Step 1: Understanding the tests of divisibility:
Divisibility by $4$ : A number is divisible by $4$ , if number formed by the last two digits (i.e., ones and tens digit) is divisible by $4$ .
Divisibility by $8$ : A number is divisible by $8$ , if number formed by the last three digits (i.e., ones, tens and hundreds digit) is divisible by $8$ .
Step 2: Check the tests of divisibility:
Consider a number $124$ .
The number formed by tens and ones digits of $124 = 24$ and which is divisible by $4$ .
The number formed by hundreds tens and ones digits of $124 = 124$ and which is not divisible by $8$
Therefore, the given statement is false.

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Similar questions

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

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

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.

State whether the following statement is True or False

All the numbers which are divisible by $4$ must also be divisible by $8$ .

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All numbers divisible by 4 must also be divisible by 8.

All numbers divisible by $4$ must also be divisible by $8 .$