Question

The highest common factor of two numbers is seven. The first number is a two digit square number and the second number is a multiple of five less than 50. What is the difference between these two numbers​

Answer 1

Since the HCF of the two numbers is 7, let the numbers be 7x and 7y where the positive integers x and y are relatively prime to each other.

Here, given that 7x is a two digit perfect square. Then x should be a multiple of 7 to satisfy this condition otherwise the number can't be a perfect square. Thus let x = 7p.

Then 7x = 49p. For the condition satisfied then p must also be a perfect square.

But if p ≥ 2² = 4, then 7x ≥ 49 × 4 = 196 > 100. Since 7x is a two digit number, p can only have the value 1. Thus 7x = 49.

And given that 7y is a multiple of 5 less than 50. Since 7 is not divisible by 5, let y = 5q for satisfying the condition. Then 7y = 35q.

If q ≥ 2, then 7y ≥ 35 × 2 = 70 > 50. So q can also take the value 1 only. Thus 7y = 35.

Now the difference between these two numbers is,

7x - 7y = 49 - 35 = 14

Hence 14 is the answer.

#answerwithquality

#BAL

Answer 2

Step-by-step explanation:

Which two numbers have 7 as a common factor?