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.
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.
Jatin007 said:
9 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.
Priya said:
1 decade ago
Factors of:
6 = 1, 2, 3.
2 = 1, 2.
They have highest common factor 2. coprime are those pair that have 1 as hcf.
So only (1,12) and (4,3) are such pairs.
6 = 1, 2, 3.
2 = 1, 2.
They have highest common factor 2. coprime are those pair that have 1 as hcf.
So only (1,12) and (4,3) are such pairs.
Sheshank said:
4 years ago
@All.
Co prime means the numbers which we take, their HCF should be 1.
If we take (2, 6) their HCF is not one so we don't consider that.
Co prime means the numbers which we take, their HCF should be 1.
If we take (2, 6) their HCF is not one so we don't consider that.
(5)
Klark said:
9 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)?
Jagrati said:
7 years ago
Product of 2 numbers = HCF * LCM.
2028= 13 * LCM.
2028/13=LCM.
Since, LCM=156.
Factors of 156 are 2*2*39.
That is the pair is 2.
2028= 13 * LCM.
2028/13=LCM.
Since, LCM=156.
Factors of 156 are 2*2*39.
That is the pair is 2.
(9)
Sujay said:
1 decade ago
No of pairs are (1, 12) , (3, 4). This is given in solution. But another pair we can consider here (4, 3) ? please explain this ?.
Xing said:
10 years ago
Longer method, divide both side by 13.
=> 13a * 13b/13 = 2028/13.
=> 13a * b = 156.
=> ab = 156/13.
=> ab = 12.
=> 13a * 13b/13 = 2028/13.
=> 13a * b = 156.
=> ab = 156/13.
=> ab = 12.
(1)
SRI said:
1 decade ago
@Veena.
I too had the doubt of 2,6.... Nice clarification given. Never though to check the HCF formed by the numbers (2, 6).
I too had the doubt of 2,6.... Nice clarification given. Never though to check the HCF formed by the numbers (2, 6).
Kishan said:
8 years ago
The product of two numbers is 2028 and their HCF is 13 If the numbers of two digits find the numbers.
Can anyone answer me?
Can anyone answer me?
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