Using Euclid’s division algorithm, find the largest number that divi

1.	Using Euclid’s division algorithm, find the largest number that divides 1251, 9377 and 15628 leaving remainders 1, 2 and 3 respectively.
Answer» From the question it’s understood that, 1251 – 1 = 1250, 9377 – 2 = 9375 and 15628 – 3 = 15625 has to be exactly divisible by the number. Thus, the required number should be the H.C.F of 1250, 9375 and 15625. First, consider 1250 and 9375 and apply Euclid’s division lemma 9375 = 1250 x 7 + 625 1250 = 625 x 2 + 0 ∴ H.C.F (1250, 9375) = 625 Next, consider 625 and the third number 15625 to apply Euclid’s division lemma 15625 = 625 x 25 + 0 We get, the HCF of 625 and 12625 to be 625. ∴ H.C.F. (1250, 9375, 15625) = 625 So, the required number is 625.

Using Euclid’s division algorithm, find the largest number that divides 1251, 9377 and 15628 leaving remainders 1, 2 and 3 respectively.

Answer»

From the question it’s understood that,

1251 – 1 = 1250, 9377 – 2 = 9375 and 15628 – 3 = 15625 has to be exactly divisible by the number.

Thus, the required number should be the H.C.F of 1250, 9375 and 15625.

First, consider 1250 and 9375 and apply Euclid’s division lemma

9375 = 1250 x 7 + 625

1250 = 625 x 2 + 0

∴ H.C.F (1250, 9375) = 625

Next, consider 625 and the third number 15625 to apply Euclid’s division lemma

15625 = 625 x 25 + 0

We get, the HCF of 625 and 12625 to be 625.

∴ H.C.F. (1250, 9375, 15625) = 625

So, the required number is 625.