Question

The product of two natural numbers is 300. The HCF of these two numbers CANNOT be (a) 2 (b) 3 (c) 5 (d) 10​

Answer 1

Answer:

HCF of two numbers is the number which is common factor for both numbers given

Here 23 is the common factor.

Other than this common factor, we also will have the product of uncommon factors for the two numbers (13 and 14 here).

The first number =23×13=299

and second number =23×14=322

Greatest of two numbers is definitely 23×14=322

Answer 2

The HCF of these two numbers CANNOT be 3 [ The correct option is (b) 3 ]

Given :

The product of two natural numbers is 300

To find :

The HCF of these two numbers CANNOT be

(a) 2

(b) 3

(c) 5

(d) 10

Solution :

Step 1 of 2 :

Write down the given data

Here it is given that product of two natural numbers is 300

Step 2 of 2 :

Choose the correct option

Check for option (a)

Let HCF of two numbers be 2

Also suppose that two numbers are 2a and 2b

By the given condition

$\displaystyle \sf 2a \times 2b = 300$

$\displaystyle \sf{ \implies }4ab = 300$

$\displaystyle \sf{ \implies }ab = 75$

Value of a and b can be natural numbers

So HCF of two numbers can be 2

So option (a) is not correct

Check for option (b)

Let HCF of two numbers be 3

Also suppose that two numbers are 3a and 3b

By the given condition

$\displaystyle \sf 3a \times 3b = 300$

$\displaystyle \sf{ \implies }9ab = 300$

$\displaystyle \sf{ \implies }ab = \frac{300}{9}$

$\displaystyle \sf{ \implies }ab = \frac{100}{3}$

Value of a and b can not be natural numbers

So HCF of two numbers can not be 3

So option (b) is correct

Check for option (c)

Let HCF of two numbers be 5

Also suppose that two numbers are 5a and 5b

By the given condition

$\displaystyle \sf 5a \times 5b = 300$

$\displaystyle \sf{ \implies }25ab = 300$

$\displaystyle \sf{ \implies }ab = 12$

Value of a and b can be natural numbers

So HCF of two numbers can be 5

So option (c) is not correct

Check for option (d)

Let HCF of two numbers be 10

Also suppose that two numbers are 10a and 10b

By the given condition

$\displaystyle \sf 10a \times 10b = 300$

$\displaystyle \sf{ \implies }100ab = 300$

$\displaystyle \sf{ \implies }ab = 3$

Value of a and b can be natural numbers

So HCF of two numbers can be 10

So option (c) is not correct

Final answer :

The HCF of these two numbers CANNOT be 3

Hence the correct option is (b) 3

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