Question

वह बड़ी से बड़ी संख्या ज्ञात क्या होगी, जिससे 590, 908 तथा 1014 को भाग दे
पर प्रत्येक दशा में समान शेष बचे।
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Answer 1

Given:

590, 908 and 1014 leaves the same remainder each time when divided by the greatest number

To find:

The greatest number

Solution:

(1). Finding the difference between the given numbers:

1014 - 908 = 106

908 - 590 = 318

1014 - 590 = 424

(2). Finding the H.C.F. of the numbers received after subtraction:

Factors:

106 = 2 × 53

318 = 2 × 3 × 53

424 = 2 × 2 × 2 × 53

H.C.F.:

H.C.F. of 106, 318 & 424 = 2 × 53 = 106

Thus, the greatest number which when divides 590, 908 and 1014 leaves the same remainder each time is → 106.

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