Question

How many numbers are co-prime to 100 and smaller than 100?
(A) 35
(C) 40
(B) 37
(D) 42​

Answer 1

Answer:

37

Step-by-step explanation:

I'm not sure but still..

Answer 2

Answer:

$\huge{\underline{\underline{\mathtt{\purple{A} \green{N}\pink{S}\blue{W}\purple{E}\red{R}}}}}$

No option is correct.

The term ‘co-prime’ doesn’t apply to a single number - it applies to sets of numbers where the set has at least 2 members.

i.e. 2 numbers can be co-prime (to each other) - which means they share no common factors.

So 2 is co-prime with all odd numbers

So 3 is co-prime with 2, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19… (missing out all those multiples of 3.

4 is co-prime with all odd numbers

5 is co-prime with all numbers that don’t have either 0 or 5 in their units place.

you can continue and build a set of co-prime numbers of each number up to 100.

for instance since 100 is 2 * 2 * 5 * 5 - 100 is co-prime with all odd numbers so long as they don’t end in 5.

99 is 3*3 * 11 - so 99 is co-prime with all numbers in your range expect for those divisible by 3, and the numbers 11, 22, 33, 44, 55, 66, 77 & 88

A quick hacked up program says there are 2944 unique co-prime pairs using the values between 2 and 100.

4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

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Hope it helps you dear!