Question

Find the largest no which exactly divide 280 and 1245 leaving remainder as 4 and 3 respectively

Answer 1

$\bold{\huge{\underline{Solution-:}}}$

Numbers = 280 and 1245

Remainders = 4 and 3

▪We will subtract the remainders from the numbers to make it completely divisible

$\implies$ 280 - 4 = 276

$\implies$ 1245 - 3 = 1242

▪Now taking LCM of both the numbers 276 and 1242

LCM = Lowest Common Factor.

▪By taking LCM we get the largest number which exactly divide 280 and 1245 leaving remainder as 4 and 3.

▪So, here is the LCM in the attachment.

LCM = 23 × 3 × 3 × 3 × 2 × 2

LCM = 2484

$\implies$ Hence 2484 is the largest which can divide both the numbers.

$\bold{\underline{Alternate\ method}}$

We can find the largest number with the help of HCF also.

By applying Euclid's division lemma

$\implies$ a = bq + r

Q = Quotient

R = Remainder

And a and b are real numbers.

1242 = 276 × 4 + 138

276 = 138 × 2 + 0

So the remainder becomes zero. Now our procedure stops. The divisor at this stage is 138. So the HCF = 138

HCF = 138

Answer 2

Answer:

138

Step-by-step explanation:

here is the answer......