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Standard V

Mathematics

Prime and Composite Numbers

If a number i...

Question

If a number is divisible by any number m , then it will also be divisible by each of the factor m'. This statement is _____ .

True

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False

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Sometimes true and sometimes false

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None of these

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Solution

The correct option is B True
If a number is divisible by a number m, It fundamentally will also by divisible by all its factors, Hence, Statement is TRUE.

For Example,
$90$ is Divisible by $45$
Factors of $45$ are $1, 3, 5, 9, 15$

$90$ is Divisible by all its Factors.

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Similar questions

Q. Study the given statements carefully. State

T

for true and

F

for false and select the correct option.

(i)

If a number is a factor of each of the given two numbers, then it must be a factor of their difference.

(i i)

If a number is divisible by another number, then it must be divisible by each of the factors of that number.

(i i i)

If a number is divisible by another number, then it is also divisible by all the multiples of that number.

(i v)

No prime number other than

2

is even but every odd number is necessarily a prime number.

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.

Q. Question 40

In the given question, state whether the given statement is True or False.

If a number a is divisible by b, then it must be divisible by each factor of b.

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.

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.

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If a number is divisible by any number m , then it will also be divisible by each of the factor m'. This statement is _____ .

The correct option is B TrueIf a number is divisible by a number m, It fundamentally will also by divisible by all its factors, Hence, Statement is TRUE.For Example,90 is Divisible by 45Factors of 45 are 1,3,5,9,1590 is Divisible by all its Factors.

The correct option is B True
If a number is divisible by a number m, It fundamentally will also by divisible by all its factors, Hence, Statement is TRUE.

For Example,
$90$ is Divisible by $45$
Factors of $45$ are $1, 3, 5, 9, 15$

$90$ is Divisible by all its Factors.