find the greatest number which on dividing 1657 and 2037 leaves a remainder 6 and 5 respectively.
(class 10 CBSE SAMPLE PAPER 2017-18 MATHS)
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To find the largest number which when divided 1657 and 2037 leaving the remainder 6 and 5. First we subtract the remainder from the given numbers and then calculate the HCF of new numbers.
Given numbers are 1657 and 2037 and remainders are 6 and 5.
New numbers after subtracting remainders are:
1657-6=1651 & 2037-5= 2032
New numbers are: 1651 & 2032
Now by using euclid's division Lemma (a=bq+r)
2032= 1651×1+ 381
1651= 381×4+ 127
381= 127×3+0
Here, Remainder= 0
Since the remainder has now become zero and the last divisior is 127.
HCF of 1651 & 2037 is 127.
Hence, required greatest number is 127.
HOPE THIS WILL HELP YOU....
Given numbers are 1657 and 2037 and remainders are 6 and 5.
New numbers after subtracting remainders are:
1657-6=1651 & 2037-5= 2032
New numbers are: 1651 & 2032
Now by using euclid's division Lemma (a=bq+r)
2032= 1651×1+ 381
1651= 381×4+ 127
381= 127×3+0
Here, Remainder= 0
Since the remainder has now become zero and the last divisior is 127.
HCF of 1651 & 2037 is 127.
Hence, required greatest number is 127.
HOPE THIS WILL HELP YOU....
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