. Find the greatest number, which divides 1442, and 1803 leaving remainder 2 and 3 respectively


a. 90

b. 180

c. 360

d. 720

Best Answer

Sol: (c)       

 Subtracting 2 from 1442 and 3 from 1803, we get

1442 – 2 = 1440 and 1803 – 3 = 1800

Now 1440 and 1800 are exactly divisible by common factors of 1440 and 1800.

The required number is the HCF of 1440 and 1800.

 By Euclid's algorithm, we have the following equations

1800 = 1400 × 1 + 360

1400 = 360 × 4 + 0

 The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 360.

HCF (1440, 1800 ) = 360

Hence the required number is 360.

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