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Find the largest number which exactly divides 280 and 1245 leaving remainders 4 and 3, respectively.
Given: 280 and 1245
To find: Here we have to find the value of the greatest number which divides 280 and 1245 leaving remainders 4 and 3 respectively.
Solution:
If the required number divide 280 and 1245 leaving remainders 4 and 3 respectively, then this means that number will divide 276(280 $-$ 4) and 1242(1245 $-$ 3) completely.
Now, we just have to find the HCF of 276 and 1242.
Finding HCF of 276 and 1242 using Euclid's division lemma:
Using Euclid’s lemma to get:
- $1242\ =\ 276\ \times\ 4\ +\ 138$
Now, consider the divisor 276 and the remainder 138, and apply the division lemma to get:
- $276\ =\ 138\ \times\ 2\ +\ 0$
The remainder has become zero, and we cannot proceed any further.
Therefore the HCF of 276 and 1242 is the divisor at this stage, i.e., 138.
So, the greatest number which divides 280 and 1245 leaving remainders 4 and 3 respectively is 138.
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