If a number on division by 56 leaves remainder 20 then the remainder obtained when same number is divided by 14 is equal to :
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Step-by-step explanation:
Suppose X be our Number, which gives remainder 20 when divided by 56. Therefore using Division Algorithm there exist a natural number q such that
X = 56q + 20
Then, X(mod 14) = (56q + 20) mod 14 = (56q mod 14 + 20 mod 14)mod 14
Note that 56q mod 14 = 0 as 56 is a multiple of 14.
and 20 mod 14 = 6 (as 20 = 14 × 3 + 6)
so, X mod 14 = 0 +6 = 6
Remark:- X mod 14 means the value of remainder when number X is divided by 14.
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