What is the greatest possible common divisor of two different positive integers which are less than 144 ?
143
142
72
71
12
143
142
72
71
12
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Integers
Source: Beat The GMAT — Problem Solving |
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thephoenix
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Take a maximum integer which is less than 144. Avoid 143 as it is a prime number.
So, consider 142. 142 has 2 prime factors => 2 and 71.
For a number less than 144 to have a 71 as prime factor, it is the number 71 itself.
So, GCD of 71 and 142 = 71 (Option D)
So, consider 142. 142 has 2 prime factors => 2 and 71.
For a number less than 144 to have a 71 as prime factor, it is the number 71 itself.
So, GCD of 71 and 142 = 71 (Option D)
Hi:
I always get confused with the untold part. The stem question makes no restrictions about primes.
Question: why can't be 143 (143x1), even if prime, it would be the greatest number (as asked).
Thank you,
Silvia
I always get confused with the untold part. The stem question makes no restrictions about primes.
Question: why can't be 143 (143x1), even if prime, it would be the greatest number (as asked).
Thank you,
Silvia
When you have 143 and any other number (say 71), GCD of 143 and 71 will be 1. Because they have only a greatest common factor of 1. 143 has only 2 factors - 1, 143. 143 cannot be a factor for some other integer less than 144.
Remember, we are asked to find the greatest possible common divisor. So, we are ignoring 143 in this problem
Remember, we are asked to find the greatest possible common divisor. So, we are ignoring 143 in this problem
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thephoenix
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- Thanked: 137 times
for 143 and 1 , 143 cant be the greatest common divisor as 143 doesnt divide 1 the GCD in this case will be 1ssuarezo wrote:Hi:
I always get confused with the untold part. The stem question makes no restrictions about primes.
Question: why can't be 143 (143x1), even if prime, it would be the greatest number (as asked).
Thank you,
Silvia
HTH
GMAT/MBA Expert
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Ian Stewart
- GMAT Instructor
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143 is not prime; it is equal to 11x13.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
ianstewartgmat.com
ianstewartgmat.com
Thank you Ian, Phoenix and Papgust.
True. They asked for the greatest common divisor, not the greatest number, and even if 143 is not prime ( didn't see it!), 11 and 13 are much lower than 71. I have to read carefully.
Thank you,
Silvia.
True. They asked for the greatest common divisor, not the greatest number, and even if 143 is not prime ( didn't see it!), 11 and 13 are much lower than 71. I have to read carefully.
Thank you,
Silvia.
