Question

If a number is divisible by 2 coprime numbers then it is divisible by their product also.

Answer 1

If a number is divisible by 2 coprime numbers then it is divisible by their product also.

The above statement is completely true.

Why ? Let's see how !

Step by step explanation :

First of all, What are Co - prime numbers ?

If the two integers, a and b has common factor as only 1 , then they are said to be Co prime numbers.

Let's prove the statement by giving some examples.

1] We know that,

80 is divisible by 4 and 5

But, now , are 4 and 5 co primes?

Let's see :

Factors of 4 => 1, 2 , 4

Factors of 5 => 1, 5

Here, Since the common factor is 1, we can say that 4 and 5 are co primes.

Now,

4 × 5 = 20

80 is also divisible by product of 4 & 5 i.e 20.

[ 80 ÷ 20 = 4 ]

_________________________

Let's see on more example.

2] 12 is divisible by 2 and 3

Factors of 2 => 1, 2

Factors of 3 => 1, 3

Common factor => 1

.•. 2 and 3 are co primes.

Now,

2 × 3 = 6

12 is also divisible by the product of 2 and 3 i. e 6

[ 12 ÷ 6 = 2 ]

Hence, Proved.

If a number is divisible by 2 coprime numbers then it is divisible by their product also.

Answer 2

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The numbers which have no other common factor other than 1 are called co-primes.

Example- The number 50 is divisible by 5 and 2

Product of 5 and 2 = 10

50 ÷ 10 = 5

Hence Proved !