Question

Find largest number which divides 318and739 leaving remender3and 4respectively

Answer 1

Step 1 : Subtract 3 and 4 from 318 and 739 respectively

318 - 3 = 315

739 - 4 = 735


Step 2 : Find the prime factors of obtained numbers

315 = 3 × 3 × 5 × 7

735 = 3 × 5 × 7 × 7


Step 3 : Find the common factors

Common factors = 3 × 5 × 7

= 105


The product of the common factors of any numbers is their HCF itself and also the least number in this question

∴ HCF = 105


∴ The largest number which divides 318 and 739 leaving remainder 3 and 4 respectively is $\boxed{\boxed{\tt{105}}}$

Answer 2

Subtract the reminders from the numbers, respectively.

318 - 3 = 315

739 - 4 = 735

Now, find the HCF of the numbers

315 = 3 × 3 × 5 × 7

735 = 3 × 5 × 7 × 7

HCF (315,735) = 3 × 5 × 7

HCF (315,735) = 105

Therefore the largest number which divides 318 and 739 leaving the reminders 3 and 4, respectively, is 105.