Find the greatest integer that divides 1251, 9377, and 15628 with remainders of 1, 2, and 3, respectively, using Euclid's division algorithm.

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450

200

625

125

answer is C.

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Detailed Solution

Given that the remainders of 1251, 9377, and 15628 are 1, 2, and 3, respectively.
So, we will subtract the remainders from the given numbers.

⇒ 1251 − 1 = 1250 ⇒ 9377 − 2 = 9375,

⇒ 15628 − 3 = 15625.

To find the HCF of 15625, 9375, and 1250.
First, we will obtain the HCF of two numbers i.e. 15625 and 9395 by using Euclid’s division algorithm.

⇒ 15625 = 9375 × 1 + 6250 ⇒ 9375 = 6250 × 1 + 3125 ⇒ 6250 = 3125 × 2 + 0

Therefore, HCF

15625, 9375 = 3125.

Now, we will obtain the HCF of 3125 and 1250 by using Euclid’s division algorithm.

⇒ 3125 = 1250 × 1 + 625 ⇒ 1250 = 625 × 2 + 0

∴ HCF

1250, 9375, 15625 = 625

Hence, the correct option is 3.

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