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Q.

The largest number that divides 1251, 9377 and 15628 leaving remainder 1, 2 and 3, respectively by using Euclid’s division algorithm is ____.


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Detailed Solution

Since 1, 2, and 3 are the remainders of 1251, 9377, and 15628.
Since we were told to leave the remainder, subtracting this remainder from the appropriate numbers gives us,
 ⇒1251−1=1250
 ⇒9377−2=9375
⇒15628−3=15625.
Now we need to find H.C.F.( 1250, 9375, 15625) which is the largest number required.
Euclid's division algorithm is a=bq+r, 0 ⩽ r < b.
Step 1: For the largest number, enter a=15625a=15625 and b=9375b=9375
⇒15625=9375×1+6250
(When we divide 15625 by 9375, we get a remainder of 6250.)
Now we take 9375 as dividend and 6250 as divisor,
 ⇒9375=6250×1+3125
(When 9375 is divided by 6250, we get 3125 as a remainder.)
Now we take 6250 as dividend and 3125 as divisor,
 ⇒6250=3125×2+0
We stop here because if we take 0 as a divisor, the solution is undefined.
So H.C.F (15625, 9375) is 3125.
Now H.C.F (3125, 1250) is equal to H.C.F (15625, 9375,1250).
Step 2: We need to find H.C.F (3125, 1250)
Now enter a=3125 and b=1250
Follow the same procedure as in step 1:
 ⇒3125=1250×2+625
⇒1250=625×2+0
The remainder is zero, so we end here.
H.C.F (15625, 9375, 1250) = 625.
625 is the largest number that divides 1251, 9377, and 15628, so the remainder is 1, 2, and 3.
So the correct answer is "625".
 
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The largest number that divides 1251, 9377 and 15628 leaving remainder 1, 2 and 3, respectively by using Euclid’s division algorithm is ____.