Question

find the largest number which divides 1251 9377 15628 and leaving remainder 1 2 3 respectively ​

Answer 1

Answer:

625

Step-by-step explanation:

Since, 1, 2 and 3 are the remainders of 1251, 9377 and 15628, respectively. Thus,

after subtracting these remainders from the numbers.

We have the numbers,

1251 – 1 = 1250,

9377 – 2 = 9375 and

15628 – 3 = 15625

Which is divisible by the required number.

Now, required number = HCF of 1250, 9375 and 15625

By Euclid’s division algorithm

= + , 0 ≤ <

For largest number, put a = 15625 and b = 9375

15625 = 9375 × 1 + 6250 [ ∵ ≠ 0 ]

⟹ 9375 = 6250 × 1 + 3125 [ ∵ ≠ 0 ]

⟹ 6250 = 3125 × 2 + 0

[Now = 0 ]

∴ HCF (15625 and 9375) = 3125

Now, we take c = 1250 and d = 3125, then again using Euclid’s division

algorithm,

= + , 0 ≤ <

   3125 = 1250 × 2 + 625

   1250 = 625 × 2 + 0

[Now = 0 ]

∴ HCF (1250, 9375 and 15625) = 625

Hence, 625 is the largest number which divides 1251, 9377 and 15628 leaving

remainder 1, 2 and 3 respectively