The H.C.F. and L.C.M. of two numbers are 25 and 500, respectively. If the first number is divided by 2, the quotient is 50 and the remainder is zero. Find the second number.
125
First find the first number. Dividing it by 2 gives quotient 50 with remainder zero, so the first number is \(2 \times 50 = 100\).
For two numbers, the product of the numbers equals the product of their HCF and LCM.
So \(\text{first} \times \text{second} = \text{HCF} \times \text{LCM} = 25 \times 500 = 12500\).
Substitute the first number 100: \(100 \times \text{second} = 12500\).
Divide to find the second number: \(\text{second} = \frac{12500}{100} = 125\).
Hence, the second number is 125.
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