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26 Dec 2025, 04:43
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We have,
2 integers up to max 212
Both are odd
Greatest common possible divisor which divides both the odd numbers. Since both are odd, they are multiples of odd numbers only.
We know that 71 x 3 = 213, which is higher than the given limit. Therefore, the answer should be less than 71.
Only possible option = 69
Both integers = 69 x 1 = 69
69 x 3 = 207
Hence, Answer Option A
2 integers up to max 212
Both are odd
Greatest common possible divisor which divides both the odd numbers. Since both are odd, they are multiples of odd numbers only.
We know that 71 x 3 = 213, which is higher than the given limit. Therefore, the answer should be less than 71.
Only possible option = 69
Both integers = 69 x 1 = 69
69 x 3 = 207
Hence, Answer Option A
26 Dec 2025, 05:00
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What is the greatest possible common divisor of two different positive integers, each less than 213, if neither of them is even?
Since neither of the numbers is even, then both numbers must be odd. The GCD of two odd numbers must also be odd.
If the GCD is x, then both numbers must be odd multiples of x. And to make GCD as large as possible, we should choose the smallest possible distinct odd multiples,like, x and 3x.
Each is less than 213
x<213
3x<213 or x<71
The largest possible odd value less than 71 is 69. Hence, our first number is 69 and second number is 69*3=207 which is also less than 213.
Greatest common divisor of (69,207) = 69
Since neither of the numbers is even, then both numbers must be odd. The GCD of two odd numbers must also be odd.
If the GCD is x, then both numbers must be odd multiples of x. And to make GCD as large as possible, we should choose the smallest possible distinct odd multiples,like, x and 3x.
Each is less than 213
x<213
3x<213 or x<71
The largest possible odd value less than 71 is 69. Hence, our first number is 69 and second number is 69*3=207 which is also less than 213.
Greatest common divisor of (69,207) = 69
26 Dec 2025, 05:39
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we check one option at a time
69 multiples= 69,138,207 ( 2 odd multiples less than 213)
71= 71,142,284 (only 1 odd multiple)
105= 105,110, 220 ( only 1 odd multiple)
Correct answer is 69
69 multiples= 69,138,207 ( 2 odd multiples less than 213)
71= 71,142,284 (only 1 odd multiple)
105= 105,110, 220 ( only 1 odd multiple)
Correct answer is 69
