find the greatest number that divises 451, 328 and 673 leaving remainders of 1, 4 and 1 respectively
Answers
Given : number divides 451, 328 and 673 leaving remainders of 1, 4 and 1 respectively
To find : Greatest possible number
Solution:
Let say greatest number = N that Divides 451 , 328 , 673 and leave remainder 1 , 4 & 1 respectively
451 = AN + 1 => AN = 450
328 = BN + 4 => BN = 324
673 = CN + 1 => CN = 672
=> N is the HCF of 450 , 324 & 672
450 = 2 * 3 * 3 * 5 * 5
324 = 2 * 2 * 3 * 3 * 3 * 3
672 = 2 * 2 * 2 * 2 * 2 * 3 * 7
HCF = 2 * 3 = 6
6 is the greatest number that Divides 451 , 328 , 673 and leave remainder 1 , 4 & 1 respectively
451 = 75 * 6 + 1
328 = 54* 6 + 4
673 = 112 * 6 + 1
6 is the greatest number
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