How many pairs of co-prime natural numbers a and b exist such that a + b = 510? Options: A . &nbsp60 B . &nbsp120 C . &nbsp64 D . &nbsp128

Answer: Option C : C 510 = 2 × 3 × 5 × 17 . Use the concept of Euler's theorem: 510 ( 1 − 1 2 ) ( 1 − 1 3 ) ( 1 − 1 5 ) ( 1 − 1 17 ) = 128 N u m b e r o f p a i r s = 128 2 = 64 .

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

Question

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

Options:

A . 60

B . 120

C . 64

D . 128

Answer: Option C
:
C

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

N u m b e r o f p a i r s = \frac{128}{2} = 64

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