The H.C.F and L.C.M of two numbers are 8 and 504 respectively.One of the numbers is 72.Determine the other.
72 = 2^3 * 3^2
504 = 72 * 7
So, now what do you think?
203
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To find out the other number, we can use the relationship between the Highest Common Factor (H.C.F) and the Least Common Multiple (L.C.M) of two numbers.
First, let's recall the definitions of H.C.F and L.C.M:
H.C.F: The Highest Common Factor is the largest number that divides two given numbers without leaving any remainder.
L.C.M: The Least Common Multiple is the smallest number that is divisible by both given numbers.
Given that the H.C.F is 8 and the L.C.M is 504, we can use the relationship between these two values.
The relationship between H.C.F, L.C.M, and the product of two numbers (in this case, x and 72) is:
H.C.F × L.C.M = Product of the numbers.
Therefore, we can write:
8 × 504 = 72 × the other number
To determine the other number, we can rearrange this equation:
the other number = (8 × 504) / 72
Calculating this expression:
the other number = 4 × 7 × 8 = 224
Hence, the other number is 224.