Find the greatest number which will divide 404, 336, 234, 200 so as to leave the same remainder in each
Case?
O 19
O 18
O 16
O 17
Answers
Given : number divide 404, 336, 234, 200 so as to leave the same remainder in each case
To Find : greatest number from given options
O 19
O 18
O 16
O 17
Solution:
Let say H is greatest Number and R is remainder
404 = HA + R
336 = HB + R
234 = HC + R
200 = HD + R
=> 68 = H (A - B)
170 = H(A - C)
204 = H (A - D)
68 = 2 x 2 x 17
170 = 2 x 5 x 17
204 = 2 x 2 x 3 x 17
HCF = 2 x 17 = 34
404 = 34 x 11 + 30
336 = 34 x 9 + 30
234 = 34 x 6 + 30
200 = 34 x 5 + 30
34 is greatest number
34 = 2x 17
from given options 17 is the greatest number which will divide 404, 336, 234, 200 so as to leave the same remainder in each Case
404 = 17 x 23 + 13
336 = 17 x 19 + 13
234 = 17 x 13 + 13
200 = 17 x 11 + 13
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