Statement Sums Involving H.C.F.
Statement Sums Involving H.C.F.
These are the following methods , used to solve the statement problems of HCF :
1. In HCF, if some remainders are given, then firstly those remainders are subtracted from the numbers given and then their HCF is calculated.
2. Sometimes in HCF questions, the required remainder is given and when the remainder is not given, in those cases you will generally have three numbers given. For answering the question, you need to take the difference of the three pairs of numbers, now the HCF of these differences will become the answer.
3. Whenever the question talks about the greatest or maximum, then in most of these cases it will be a question of HCF. Secondly, whenever the question is related to classification or distribution into groups, then in all the cases it is HCF only.
Illustration 1 : Find the greatest number which when divides 259 and 465 leaves remainders 4 and 6 respectively.
Solution: Here, the numbers 259 and 465 leave the remainders 4 and 6 respectively. So, the required number will be obtained by finding the H.C.F. of 259 – 4 = 255 and 465 – 6 = 459.
Factors of 255 = 5 51 and Factors of 459 = 3
3
51.
The HCF of 255 and 459 is 51 which is the number.
Illustration 2 : Find the greatest number, which when divides 41, 71 and 91, leaves the same remainder in each case.
Solution: Take the difference between all the three pairs of numbers and their HCF will be the answer i.e. 91 – 41 = 50, 71 – 41 = 30 and 91 – 71 = 20.
Factors of 50 = 2 5
5 , Factors of 30 = 2
3
5 and factors of 20 = 2
2
5
The HCF of 50, 30 and 20 is 10.
Find the largest number that divides 2053 and 967 and leaves a remainder of 5 and 7 respectively. | |||
| Right Option : C | |||
| View Explanation | |||
Find the greatest number which when divides 150 and 392 leaves remainders 4 and 6 respectively. | |||
| Right Option : C | |||
| View Explanation | |||
Find the greatest number, which when divides 15 , 21 and 27, leaves the same remainder in each case. | |||
| Right Option : A | |||
| View Explanation | |||
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