Question

Find the largest number which exactly divides 280 and 1245 leaving remainders 4 and 3, respectively.

Answer 1

SOLUTION:

To find the greatest number which when divides 280 and 1245 leaving the remainders 4 and 3 respectively.  First ,we subtract the remainder from the given numbers and then calculate the HCF of new numbers.

Given numbers are  280 and 1245 and  remainders are 4 and 3.

Then ,new numbers after subtracting remainders are :

280 - 4 = 276 and 1245 - 3 = 1242

Now, we have to find the H.C.F. of 276 and 1242.

By applying Euclid’s division lemma,a = bq+r

Let a = 1242 and b = 276

1242 = 276 x 4 + 138

276 = 138 x 2 + 0.

Here remainder is zero , and the last divisor is 138.

So H.C.F is 138

Hence, the required greatest number is 138

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Answer 2

We Subtract The Required Remainders From Their Corresponding Numbers

280-4 = 276

1245-3 = 1242

We Find Their Hcf

Hcf Of 276 And 1242   => 138

So 138 Is The Required Number

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according to this question
280-4=276       and   1245-3=1242 

and finding their HCF separetely 

280=2*2*3*23
1242=2*3*3*3*23

HCF[276,1242]=2*3*23
                       =138
THUS 138 is the largest number which exactly divides 280 and 1245 leaving remainder 4 and 3 hence found


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