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. 1)
1.
Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
Answer: Option
Explanation:
Required number = H.C.F. of (91 - 43), (183 - 91) and (183 - 43)
= H.C.F. of 48, 92 and 140 = 4.
Discussion:
210 comments Page 3 of 21.
Shreekanth said:
7 years ago
Keep on dividing all the three numbers by 2 so that reminder should be the same ie
2[43 91 183]
[ 21 45 91] remainder will be 1 for all the three.
Divide again by 2.
2[21 45 91]
10 22 45 remainders will be same ie 1.
So after this, if you try to divide all three again by 2 then you get a different value for the reminder.
And hence; 2 * 2 = 4.
2[43 91 183]
[ 21 45 91] remainder will be 1 for all the three.
Divide again by 2.
2[21 45 91]
10 22 45 remainders will be same ie 1.
So after this, if you try to divide all three again by 2 then you get a different value for the reminder.
And hence; 2 * 2 = 4.
(1)
SAROJA said:
1 decade ago
43 = HA+R.
91 = HB+R.
183 = HC+R.
Here we are expressing the numbers as HCF*Prime number.
43-91 = H(A-B) = 48.
183-91 = H(C-B) = 92.
183-43 = H(C-A) = 140.
So when we take HCF of 48, 92, 140 we get "H".
*When we are expressing two numbers in terms of their HCF the format is HCF*co-primes. So we have expressed.
43 = HA, 91 = HB, 183 = HC.
91 = HB+R.
183 = HC+R.
Here we are expressing the numbers as HCF*Prime number.
43-91 = H(A-B) = 48.
183-91 = H(C-B) = 92.
183-43 = H(C-A) = 140.
So when we take HCF of 48, 92, 140 we get "H".
*When we are expressing two numbers in terms of their HCF the format is HCF*co-primes. So we have expressed.
43 = HA, 91 = HB, 183 = HC.
Abrar said:
1 year ago
By division method:
43)183(4
172
-----
11)43(3
33
------
10)11(1
10
-----
1)10(10
10
------
0
Now use the last divisor with the mid-number 1.
You get again the remainder as a 0,
Hence 1 should be the answer.
43)183(4
172
-----
11)43(3
33
------
10)11(1
10
-----
1)10(10
10
------
0
Now use the last divisor with the mid-number 1.
You get again the remainder as a 0,
Hence 1 should be the answer.
(21)
RAJ said:
1 decade ago
Actually hcf means highest common factor.
Which means"highest number which divide the numbers leaving reminder as 0".
Look at the question they asked to find a hcf which leaves the sme reminder in each case.
By outer observation we can say 4 is hcf because 43/4=3, 91/4=3, and 143/4=3.
Its a simple method of analysing hcf.
Which means"highest number which divide the numbers leaving reminder as 0".
Look at the question they asked to find a hcf which leaves the sme reminder in each case.
By outer observation we can say 4 is hcf because 43/4=3, 91/4=3, and 143/4=3.
Its a simple method of analysing hcf.
Sanjana said:
3 years ago
The H.C.F is 1.
The prime factorization of 43 is 43 as it is a prime number.
The prime factorization of 91 is 7 and 3.
The prime factorization of 183 is 3 and 61.
There is no common numbers between these 3 numbers. But,1 is a common factor for each and every number. In this case, 1 is the H.CF.
The prime factorization of 43 is 43 as it is a prime number.
The prime factorization of 91 is 7 and 3.
The prime factorization of 183 is 3 and 61.
There is no common numbers between these 3 numbers. But,1 is a common factor for each and every number. In this case, 1 is the H.CF.
(52)
Komal said:
1 decade ago
The difference is used to get the common factors between two nos. it will eliminate the uncommon factors.
And at-last we have only to pick up the highest common factor...
you can try with an example for 30 and 10.
factors of (30) = 5,2,3
factors of (10) = 5,2
factors of (30-10) = 5,2
And at-last we have only to pick up the highest common factor...
you can try with an example for 30 and 10.
factors of (30) = 5,2,3
factors of (10) = 5,2
factors of (30-10) = 5,2
Mysterious said:
1 decade ago
@Mini and all friends
If it was just asked to find the HCF of 43,91,183 then simply the Division method or Factorization method had been applied.
But here it is stated that "so as to leave the same remainder in each case", that's why the difference of the numbers is calculated.
If it was just asked to find the HCF of 43,91,183 then simply the Division method or Factorization method had been applied.
But here it is stated that "so as to leave the same remainder in each case", that's why the difference of the numbers is calculated.
Mani pandian said:
1 decade ago
Here are the list of prime factors of 24 and 36:
24 = 2 x 2 x 2 x 3.
36 = 2 x 2 x 3 x 3.
If we write down the numbers that are the same in both lists, they will give us the highest common factor of 24 and 36:
HCF of 24 and 36 is 2 x 2 x 3 = 12.
This is the meaning of H.C.F.
24 = 2 x 2 x 2 x 3.
36 = 2 x 2 x 3 x 3.
If we write down the numbers that are the same in both lists, they will give us the highest common factor of 24 and 36:
HCF of 24 and 36 is 2 x 2 x 3 = 12.
This is the meaning of H.C.F.
Manoj Rmk said:
9 years ago
Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
Explanation: 43, 91, 183.
183 = (183-91) = 92.
91 = (183-43) = 140.
43 = (91-43) = 48.
92, 140, 48.
92 = 2 * 2 * 23.
140 = 2 * 2 * 35.
48 = 2 * 2 * 2 * 3 * 2.
Ans 4.
Explanation: 43, 91, 183.
183 = (183-91) = 92.
91 = (183-43) = 140.
43 = (91-43) = 48.
92, 140, 48.
92 = 2 * 2 * 23.
140 = 2 * 2 * 35.
48 = 2 * 2 * 2 * 3 * 2.
Ans 4.
Govind Paswan said:
1 decade ago
Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
Explanation: 43, 91, 183.
183 = (183-91) = 92.
91 = (183-43) = 140.
43 = (91-43) = 48.
92, 140, 48.
92 = 2*2*23.
140 = 2*2*35.
48 = 2*2*2*3*2.
Ans 4.
Explanation: 43, 91, 183.
183 = (183-91) = 92.
91 = (183-43) = 140.
43 = (91-43) = 48.
92, 140, 48.
92 = 2*2*23.
140 = 2*2*35.
48 = 2*2*2*3*2.
Ans 4.
(1)
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