Aptitude - Problems on H.C.F and L.C.M - Discussion

Discussion :: Problems on H.C.F and L.C.M - General Questions (Q.No.22)

22. 

Three numbers which are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is:

[A]. 75
[B]. 81
[C]. 85
[D]. 89

Answer: Option C

Explanation:

Since the numbers are co-prime, they contain only 1 as the common factor.

Also, the given two products have the middle number in common.

So, middle number = H.C.F. of 551 and 1073 = 29;

First number = 551 = 19;    Third number = 1073 = 37.
29 29

Required sum = (19 + 29 + 37) = 85.


Anjali said: (Dec 21, 2010)  
I didn't understand this question. Please help me.

Aparna said: (Dec 29, 2010)  
Nothing to worry,

see in HCF we get a number which is common to both numbers.

So find the hcf of 551 and 1073, we get 29

which is one number among three nos.

Let other two numbers be a and b

Given
a*29=551
a=551/29
a=19

Now,
b*29=1073
b=37

Hence three numbers. are 29,19,37

Vishnu said: (Jan 17, 2011)  
Awesome way of explaining :-)

Uttam said: (Feb 3, 2011)  
Consider numbers as X, Y, Z respectively.

Now,

Consider product XY = 551 ------eq1
Consider product YZ = 1073 -----eq2

So,clearly common highest factor btw XY and YZ should be Y

i.e HCF (551,1073) = 29.

From eq 1, X=19.
from eq 2, Y=37.

Pls comment if my assumption is wrong.

Vinayak said: (Sep 5, 2011)  
@uttam. You are right.

Sangeeta said: (Dec 2, 2011)  
How to know that 29 is the common factor?

Please tell me?

Prasant said: (Dec 30, 2011)  
How to find 29 ? Is there any shortest way?

Ashutosh said: (May 23, 2012)  
Hello friends its simple to get 29.

1 step:-1073-551 we will get 522.
Now,
2 step:- 551-522 we will get 29

Rahul said: (Mar 4, 2013)  
Can any one tell me how to calculate HCF/LCM of big numbers in easy way?

Mustafa Ahmed said: (Aug 27, 2013)  
How to find 29? Please show the divided process.

Gopi said: (Oct 28, 2013)  
In-case of co primes, if 29 is the middle number then first should be 23 and last should be 31. Then the given values not match. Please clarify.

Venkatareddy said: (Feb 11, 2014)  
How the you can say 29 is the common factor and explain?

Prathyusha.J said: (Mar 8, 2014)  
@Gopi.

If we take the numbers to be 23 and 31,

We get 23*29=667.. which is in contrast with the question.

So the numbers should be 19 and 37.

Sathiya Priya said: (Jul 14, 2014)  
Let assume three numbers are a, b and c.

Given:

The product of a and b is 551.

The product of b and c is 1073.

b is common in both the product

b = H.C.F. of 551 and 1073 = 29;

a = (551/29) = 19.
c = (1073/289) = 37.

The sum of three number is 85.

Sujeeth said: (Jul 11, 2015)  
Explain how 29 came?

Soni said: (Mar 27, 2016)  
Please, explain the problem clearly.

Jyoti. said: (Apr 19, 2016)  
@Sujeeth

1*3 = 3
5*7 = 35
5*0 = 0
1.
= 3 - 35 - 0 - 1.
= 28 - 0 - 1.
= 28 + 1.
= 29.

Neharika said: (Jun 5, 2016)  
Four prime numbers are arranged in ascending order according to their magnitude. The product of first Three is 20,677 and the product of last three 33,263. Find the numbers.

Can anyone solve and explain this question ?

Aby said: (Jun 18, 2016)  
Thank you, @Ashutosh.

Samir said: (Jul 12, 2016)  
Why we divide 29 from 551 & 1073?

Mahi said: (Jul 25, 2016)  
Good and clear explanation @Ashutosh.

Krishna said: (Aug 13, 2016)  
@Jyoti, Can you explain it clearly?

Rudrika said: (Aug 14, 2016)  
@Ashutosh,

Your explanation is very nice.

Anant said: (Aug 19, 2016)  
Thanks @Ashutosh.

Ranjith said: (Aug 28, 2016)  
xy = 551 & yz = 1073; clearly y is a HCF.

Multiply xy * yz = 1073 * 551 we get xzy^2 = 29sqroot703;

So 29 is y; then it is easy to proceed .

Preethi said: (Aug 29, 2016)  
I can't understand how 29 comes?

Ram said: (Sep 2, 2016)  
29 is the HCF of 551 and 1073.

To find HCF of 551 and 1073 follow these steps.

551)1071(1
551
----------------
522)551(1
522
------------
29)522(18
29
---------
232
232
------------
XXX

So,HCF of 551 and 1073 is 29.

Anonymous said: (Oct 5, 2016)  
How will the solution change if the given numbers are not co-prime?

Tanvir said: (Dec 1, 2016)  
Which least number should be added to 2497 so that the sum is exactly divisible by 3, 4, 5, and 6?

Solve it and find the answer.

Purva said: (Dec 13, 2016)  
@Tanvir.

2497/60 we get remainder as 37.
Now: LCM of 5, 6, 4, 3 is 60.
(60 - 37) = 23.

Diksha said: (Jan 4, 2017)  
Why the 29 divided the term. It's middle term but what logic behind this?

Ajit said: (Jun 12, 2017)  
Let me explain (551-1071) = 522 then again least no minus (551-522) = 29.

Divyanshu Priyadarshi said: (Aug 20, 2017)  
Let the three numbers be x, y and z.

Hence, xy=551 and yz=1073.
Middle number =HCF of 551 and 1073 = 29.
First number =551/29= 19.
Third number =1073/29= 37.
Required numbers are 19,29 and 37.

Surya Deep said: (Aug 20, 2017)  
Consider numbers as X, Y, Z respectively.

Now,

Consider product XY = 551 ------eq1
Consider product YZ = 1073 -----eq2

So, clearly common highest factor btw XY and YZ should be Y
i.e HCF (551,1073) = 29.

From eq 1, X=19.
from eq 2, Z=37.

Now, Add this numbers (X+Y+Z)
(19+29+37)=85 And.

Asaduzzaman said: (Dec 18, 2017)  
Thanks.

Muhammad Safeer Ahmed said: (May 11, 2018)  
a*b=551
b*c=1073

So, b is =1073-551=522,
522-551=29,
29 is middle and common term exist in both and b =29.

Put the value
a*b=551
a*29=551
a=551/29=19
a=19.

Put the value
b*c=1073
29*c=1073
C=1073/29=37.

So
a=19
b=29
c=37
19+29+37=85.

Anamika said: (Jul 8, 2018)  
Thanks all for the answer.

Dinu said: (Sep 28, 2018)  
@Jyoti.

30-1 = 29.
So,
80+5=85.

Abhoi said: (Dec 16, 2018)  
Thanks @Asutosh.

Tanu said: (Jan 4, 2019)  
Why we take HCF why not LCM? Please explain me.

Shaurya said: (Jan 17, 2019)  
Let the three no be a,b,c.

a*b=551
a*b=19*29

Now
b*c=1073
b*c=29*37

So we get a=19,b=29 and c=37.
On adding a+b+c=19+29+37=85.

Kalpit said: (Feb 2, 2019)  
Good explanatiion, Thanks @Uttam.

Animo said: (Mar 24, 2019)  
Thanks @Safeer.

Shreya said: (Oct 23, 2019)  
I don't understand why we take the HCF of 551 and 1073.

Nivi said: (Mar 29, 2020)  
Let me explain.

Co-prime : factors are 1 and itself.

Given: XY=551.
YZ=1073.

Since why is a common factor in both the equations and the as the no's are caprice then the other factor becomes the highest common factor.

So, Y is the HCF of XY and YZ.

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