• what is the smallest no. that when divided by 35,56,91 leaves remainders of 7 in each case?
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Subtract 7 from 35 , 56 and 91 .
Therefore --
35 - 7 = 28 ....................... 1
56 - 7 = 49 ....................... 2
91 - 7 = 84 ........................ 3
So for smallest number we need to find HCF of new numbers
28 = 2 × 2 × 7
49 = 7 × 7
84 = 2 × 2 × 3 × 7
Therefore HCF = 7
So the smallest number is 7 .
Therefore --
35 - 7 = 28 ....................... 1
56 - 7 = 49 ....................... 2
91 - 7 = 84 ........................ 3
So for smallest number we need to find HCF of new numbers
28 = 2 × 2 × 7
49 = 7 × 7
84 = 2 × 2 × 3 × 7
Therefore HCF = 7
So the smallest number is 7 .
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