The H.C.F of two numbers is 70. Their product is 49000. What is the difference between the two numbers?
70a * 70b = 49000
ab = 10
see what you can do with that
To find the difference between the two numbers, we need to determine what the two numbers are. We have been given that their highest common factor (H.C.F) is 70 and their product is 49000.
To find the two numbers, we can use the formula: Product = H.C.F × L.C.M (Least Common Multiple).
We already know the product (49000) and the H.C.F (70), so we can substitute these values into the formula to solve for the L.C.M.
49000 = 70 × L.C.M
Now, let's calculate the L.C.M by dividing both sides of the equation by 70:
L.C.M = 49000 ÷ 70
L.C.M = 700
So, the L.C.M of the two numbers is 700.
Now that we know the L.C.M, we can find the two numbers by dividing the product by the L.C.M:
Number 1 = Product ÷ L.C.M
Number 1 = 49000 ÷ 700
Number 1 = 70
Number 2 = Product ÷ Number 1
Number 2 = 49000 ÷ 70
Number 2 = 700
Hence, the two numbers are 70 and 700.
To find the difference between the two numbers, we subtract the smaller number from the larger number:
Difference = Larger Number - Smaller Number
Difference = 700 - 70
Difference = 630
Therefore, the difference between the two numbers is 630.