Question

How many pairs of co-prime natural numbers a and b exist such that a + b = 510?

• A. 60
• B. 120
• C. 64
• D. 128

Answer 1

The correct option is C

64

$510=2\times 3\times 5\times 17$.
Use the concept of Euler's theorem:
$510(1-\frac{1}{2})(1-\frac{1}{3})(1-\frac{1}{5})(1-\frac{1}{17})=128$
$Numberofpairs=\frac{128}{2}=64$.