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Greatest common divisor
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SoCan
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The quickest way to do a question like this if you get it on a test is probably just to go through the answers. I'll try to rephrase the given explanation somewhat, but it's difficult to say it too differently.
1 - the only number less than 144 than has 143 as a factor is 143 - the question asks for a common factor of TWO DIFFERENT integers
2 - same rationale as above - 142 is the only number less than 144 with 142 as a factor.
3 - same rationale as above, but it's trying to trick you. 72 is the only number less than 144 with 72 as a factor, but you might want to select this one because it's also a factor of 144. However, remember that the two integers must be LESS than 144.
4 - 71 is a factor of 71 and 142. 142 is less than 144, so 71 is the answer.
1 - the only number less than 144 than has 143 as a factor is 143 - the question asks for a common factor of TWO DIFFERENT integers
2 - same rationale as above - 142 is the only number less than 144 with 142 as a factor.
3 - same rationale as above, but it's trying to trick you. 72 is the only number less than 144 with 72 as a factor, but you might want to select this one because it's also a factor of 144. However, remember that the two integers must be LESS than 144.
4 - 71 is a factor of 71 and 142. 142 is less than 144, so 71 is the answer.
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Anurag@Gurome
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venmic wrote:Any explanations for this one. I need a simpler way to undersand it
Solution:
Let the gcd of the two integers be d and let the integers be da and db where a and b are co-prime and distinct.
So, the possible combinations of a and b are (1,2),(1,3),(2,3)....
So, da and db can be (d,2d),(d,3d),(2d,3d).....
If da and db are (d,2d), d < 144 and 2d < 144. Since d is maximum, 2d = 142 and d is 71.
If da and db are (d,3d), d < 144 and 3d < 144. Since d is maximum, 3d = 141 and d is 47.
We can see that every other combination of da and db gives lesser and lesser value of d.
Or (d, 2d) such that 2d = 142 will give the largest value of d which is 71.
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144 can be expressed as 1*144 or 2*72.
If it was 144, 72 could be a divisor.
Since we are looking at numbers that are less than 144, any number close to 72 would be the answer. From the answer choices 71 is close. So the answer is 71.
If it was 144, 72 could be a divisor.
Since we are looking at numbers that are less than 144, any number close to 72 would be the answer. From the answer choices 71 is close. So the answer is 71.
