Question

Two numbers are in the ratio 21:17. If their HCF is 5, find the numbers.​

Answer 1

Answer:

Given :-

• Two numbers are in the ratio of 21 : 17 and their HCF is 5.

To Find :-

• What are the numbers.

Solution :-

Let, the first number be 21x

And, the second number will be 17x

Then, the L.C.M = 21x × 17x

As we know that,

✪ H.C.F × L.C.M = Product of two numbers ✪

Given :

• H.C.F = 5
• L.C.M = 21x × 17x
• Product of two numbers = 21x and 17x

According to the question by using the formula we get,

⇒ 5 × 21x × 17x = 21x × 17x

⇒ 5 × 357x = 357x

⇒ 5 = 357x/357x

⇒ 5 = x

➠ x = 5

Hence, the required numbers are,

✧ First number = 21x = 21(5) = 105

✧ Second number = 17x = 17(5) = 85

∴ The numbers are 105 and 85.

Answer 2

Solution:-

Given:-

• → Ratio are 21 : 17
• → Let the be 21x , 17x and its HCF be x
• → Its HCF is 5
• → Number 21x , 17x , where x is 5

We Get

• → 21x and 17x
• → 21 × 5 and 17 × 5
• → 105 and 85
• → The Number are 105 and 85

Answer

• 105 and 85

                                                       

More Information about HCF

→ HCF( Highest common factor )  of two or more number cannot greater than any one of them

→ If One number is a factor of the other number their HCF will be that Smaller number

→The HCF of the Number is the product of the common prime factor