Aptitude - Problems on H.C.F and L.C.M - Discussion
Discussion Forum : Problems on H.C.F and L.C.M - General Questions (Q.No. 9)
9.
The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:
Answer: Option
Explanation:
Let the numbers 13a and 13b.
Then, 13a x 13b = 2028
ab = 12.
Now, the co-primes with product 12 are (1, 12) and (3, 4).
[Note: Two integers a and b are said to be coprime or relatively prime if they have no common positive factor other than 1 or, equivalently, if their greatest common divisor is 1 ]
So, the required numbers are (13 x 1, 13 x 12) and (13 x 3, 13 x 4).
Clearly, there are 2 such pairs.
Discussion:
94 comments Page 3 of 10.
Sami said:
9 years ago
How to choose the pairs?
Gogul said:
9 years ago
I think the question have its answer.
The product of two numbers is 2028.
The Number of such pairs is 2.
Whatever it is, only 2 pairs, because we have only a and b, if we have a, b, c, d then we may have more pairs.
2 x 6
3 x 4
4 x 3
1 x 12
12 x 1
6 x 2
Correct me if I'm wrong.
The product of two numbers is 2028.
The Number of such pairs is 2.
Whatever it is, only 2 pairs, because we have only a and b, if we have a, b, c, d then we may have more pairs.
2 x 6
3 x 4
4 x 3
1 x 12
12 x 1
6 x 2
Correct me if I'm wrong.
Snehesh said:
9 years ago
I followed this method:
13a * 13b = 2028.
13ab = 2028.
ab = 156.
Now try to find the unique pairs (Prime factorize) forming 156:
2 * 78, 3 * 52.
So there are just 2 pairs. Hence, ans is 2.
13a * 13b = 2028.
13ab = 2028.
ab = 156.
Now try to find the unique pairs (Prime factorize) forming 156:
2 * 78, 3 * 52.
So there are just 2 pairs. Hence, ans is 2.
Shobs said:
9 years ago
Only 2 pairs is correct. Know the meaning of co-prime first "two numbers are said to be coprime if their H.C.F is 1 "which suits only the (1, 12) and (3, 4) pairs.
Sai ravi teja vallabhuni said:
9 years ago
Guys, 2 and 6 are not co-primes, that means 2 is divided only by 1 and 6 is divided by both 2 and 3.
Co primes are the numbers where they should be divided only by one, in this case, they are 3 and 4.
Co primes are the numbers where they should be divided only by one, in this case, they are 3 and 4.
Vinay ambidi said:
10 years ago
No someone asked why 5, 7 but if we multiply those numbers we will get 5*7 = 35.
That's why we have to take 1, 12 or 3, 4.
That's why we have to take 1, 12 or 3, 4.
Yashraj said:
8 years ago
I can't understand this. Please help me to get it.
Jatin007 said:
8 years ago
Another way I'm telling you without co-primes.
2028/13=156, again divide 156/13 = 12.
Now factorize 12 = 1, 12, 3, 4.
There are 4 numbers so the pair is 2.
2028/13=156, again divide 156/13 = 12.
Now factorize 12 = 1, 12, 3, 4.
There are 4 numbers so the pair is 2.
Klark said:
8 years ago
Why we can't use the pair (4, 3) & (12, 1). We are asked to find the total number of such pairs. So (1, 12), (3, 4), (4, 3), (12, 1)?
Garima said:
8 years ago
Can we take a pair of 13, 1?
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