- Home/
- SSC & Railways/
- Article
Find the largest number which on dividing 1251, 9377 and 15628 leaves remainders 1, 2 and 3 respectively.
By BYJU'S Exam Prep
Updated on: September 25th, 2023
625 is the largest number which on dividing 1251, 9377 and 15628 leaves remainders 1, 2 and 3 respectively. To know how we get this answer, refer to the detailed solution below. The method used to define the answer is Euclid’s Dilemma which is used to find out the highest common factor between two or more numbers.
Table of content
Largest Number Divisible By 1251, 9377 and 15628
to calculate the largest number dividing 1251, 9377 and 15628 and leaving remainders 1, 2 and 3 respectively, we will use Euclid’s dilemma.
For it, we will first subtract the numbers with their respective remainders –
1251 – 1 = 1250
9377 – 2 = 9375
15628 – 3 = 15625
Now, from these newly derived numbers, we will find the HCF using Euclid’s Dilemma –
9375 = 1250 × 7 + 625
Here, we have the remainder which is not zero,
Thus, now we will divide 1250 and 625 –
1250 = 625 × 2 + 0
We now have the zero as a reminder when we divide 1250 by 625. Thus, HCF (1250, 9375) is 625.
The next step is to calculate the HCF of 15625 and 625 which we will divide in the following way –
15625 = 625 × 25 + 0
The remainder is again zero. Hence, HCF (15625, 625) is 625.
From these calculations, we have found that the HCF (1250, 9375, 15625) is 625.
Thus, 625 is the answer.
Euclid’s Method
Euclid’s dilemma is a division method that helps find the HCF of two or more numbers. As per this method, there are two positive integers, let’s say, a and b. With them, there also exist unique integers q and r where q is the quotient and r is the remainder, with both being distinct. According to this method, a = bq + r, 0≤ r
Summary:
Find the largest number which on dividing 1251, 9377 and 15628 leaves remainders 1, 2 and 3 respectively.
The largest number that divides 1251, 9377 and 15628 leaving 1, 2 and 3 as remainders is 625. We calculated this answer by finding out the HCF of all these numbers by using Euclid’s Dilemma.
Related Questions:
- Find the largest number which divides 70 and 125 leaves remainders 5 and 8 respectively.
- Find the largest number that will divide 398 , 436 and 542 leaving remainders 7 , 11 and 15 respectively
- Find the greatest number that will divide 445, 572 and 699 leaving remainder 4,5,6 effectively
- What is the largest number that divides 245 and 1029, leaving remainder 5 in each case?
- What is the smallest number that, when divided by 35, 56 and 91 leaves remainder of 7 in each case
- A Car Traveling at 20 Kmh Speeds Up to 60 Kmh in 6 Seconds What is Its Acceleration in Ms2
- Factorize the Equation: x^3-3x^2-9x-5
