Check if the given set of numbers is exactly divisible by $4$ . If yes , then find out whether the sum and difference of the two numbers are also exactly divisible by $4$ .
$64$ and $16$

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Solution

Given, the numbers are $64$ and $16$
Now, $64 \div 4 = 16$
$16 \div 4 = 4$
Yes, the given numbers are divisible by $4$
Now, the sum of two numbers are :- $64 + 16 = 80$
and the difference of two numbers are :- $64 - 16 = 48$
Now , $80 \div 4 = 20$
$48 \div 4 = 12$
Hence, the sum and difference of two numbers are also exactly divisible by $4$ .

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Q. Write (T) for true and (F) for false against each of the following statements:
(i) If a number is divisible by 4, it must be divisible by 8.
(ii) If a number is divisible by 8, it must be divisible by 4.
(iii) If a number divides the sum of two numbers exactly, it must exactly divide the numbers separately.
(iv) If a number is divisible by both 9 and 10, it must be divisible by 90.
(v) A number is divisible by 18 if it is divisible by both 3 and 6.
(vi) If a number is divisible by 3 and 7, it must be divisible by 21.
(vii) The sum of two consecutive odd numbers is always divisible by 4.
(viii) If a number divides two numbers exactly, it must divide their sum exactly.

Q. Which of the following statements are true?

(i) If a number is divisible by 3, it must be divisible by 9.
(ii) If a number is divisible by 9, it must be divisible by 3.
(iii) If a number is divisible by 4, it must be divisible by 8.
(iv) If a number is divisible by 8, it must be divisible by 4.
(v) A number is divisible by 18, if it is divisible by both 3 and 6.
(vi) If a number is divisible by both 9 and 10, it must be divisible by 90.
(vii) If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately.
(viii) If a number divides three numbers exactly, it must divide their sum exactly.
(ix) If two numbers are co-prime, at least one of them must be a prime number
(x) The sum of two consecutive odd numbers is always divisible by 4.

Which of the following statements are true ?
(i) If a number is divisible by 3, it must be divisible by 9.
(ii) If a number is divisible by 9, it must be divisible by 3.
(iii) If a number is divisible by 4, it must be divisible by 8.
(iv) If a number is divisible by 8, it must be divisible by 4.
(v) A number is divisible by 18, if it is divisible by both 3 and 6.
(vi) If a number is bivisible by both 9 and 10, ut nyst be divisible by 90.
(vii) If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately.
(viii) If a number divides three numbers exactly, it must divede their sum exactly.
(ix) If two numbers are co-prime , at least one of them must be a prime number.
(x) The sum of two consecutive odd numbers is always divisible by 4.

Check if the given set of numbers is exactly divisible by $4$ . If yes , then find out whether the sum and difference of the two numbers are also exactly divisible by $4$

$88$ and $36$

Q. Choose the correct statements
S1: All the numbers divisible by 10 are also divisible by 5.
S2: A number divisible by 3 is also divisible by 6.
S3: A number is divisible by 7, if the last two digits are divisible by 7.
S4: If a number divides the product of two numbers exactly then it must exactly divide the numbers separately.
S5: If a number exactly divides two numbers separately, and after division, if its difference is taken then this difference will also be exactly divisible by that number.

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Check if the given set of numbers is exactly divisible by 4. If yes , then find out whether the sum and difference of the two numbers are also exactly divisible by 4.64 and 16

Given, the numbers are 64 and 16Now, 64÷4=1616÷4=4Yes, the given numbers are divisible by 4Now, the sum of two numbers are :- 64+16=80and the difference of two numbers are :- 64-16=48Now ,80÷4=2048÷4=12Hence, the sum and difference of two numbers are also exactly divisible by 4.

Check if the given set of numbers is exactly divisible by $4$ . If yes , then find out whether the sum and difference of the two numbers are also exactly divisible by $4$ .
$64$ and $16$