Postal charges are Rs 20, Rs 28 and Rs 36. If stamps of one denomination are to be used, what is the greatest denomination needed?
Rs 4
Goal: Use stamps of one value to make Rs 20, Rs 28, and Rs 36 exactly.
This value must divide all three numbers. So find the HCF/ GCD of 20, 28, 36.
Step 1: Prime factorize each amount
\(20 = 2 \times 2 \times 5\)
\(28 = 2 \times 2 \times 7\)
\(36 = 2 \times 2 \times 3 \times 3\)
Step 2: Take only the primes common to all
Common primes: \(2\) and \(2\)
Step 3: Multiply the common primes
\(2 \times 2 = 4\)
Conclusion
The greatest stamp value that fits all is \(\boxed{4}\). So denomination needed = Rs 4.