Using Euclid’s division algorithm, find the largest number that divides 1251, 9377 and 15628 leaving remainders 1, 2 and 3, respectively
Solution:
The remainders of 1251, 9377 and 15628 are 1, 2 and 3
By subtracting these remainders from the numbers, we get
1251 - 1 = 1250,
9377 - 2 = 9375
15628 - 3 = 15625,which are divisible by the required number.
Required number = HCF (1250, 9375, 15625).
Using Euclid’s division algorithm,
a = bq + r --- (i)
We know that dividend = divisor x quotient + remainder
Consider a = 15625 and b = 9375
15625 = 9375 × 1 + 6250 [from eq. (i)]
9375 = 6250 × 1 +3125
6250 = 3125 × 2 + 0
HCF (15625, 9375) = 3125.
Taking c = 1250 and d = 3125,
Again by using Euclid’s division algorithm, d = cq + r
3125 = 1250 × 2 + 625
1250 = 625 × 2 + 0
HCF (1250, 9375,15625) = 625
Therefore, 625 is the largest number which divides 1251, 9377 and 15628 leaving remainders, 1, 2 and 3, respectively.
✦ Try This: Using Euclid’s division algorithm, find the largest number that divides 730, 245 and 2190 leaving remainders 1, 2 and 3, respectively
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 1
NCERT Exemplar Class 10 Maths Exercise 1.3 Problem 9
Using Euclid’s division algorithm, find the largest number that divides 1251, 9377 and 15628 leaving remainders 1, 2 and 3, respectively
Summary:
Using Euclid’s division algorithm,625 is the largest number which divides 1251, 9377 and 15628 leaving remainders, 1, 2 and 3, respectively
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