Question

find the largest two digit number that divides 673 and 865 leaving remainder 1 in each

Answer 1

Answer :-

Subtract the remainders from their respective divisors :-

■ 673 - 1 = 672

■ 865 - 1 = 864

HCF of 672 and 864 -

=》 $\sf{864 = 672 × 1 + 192}$

=》 $\sf{672 = 192 × 3 + 96}$

=》 $\sf{192 = 96 × 2 + 0}$

$\tt{Divisor = 96}$

Answer = $\huge{\sf{96}}$

Answer 2

Find the largest two digit number that divides 673 and 865 leaving remainder 1 in each.

Answer : 96

Step by step explanation :

In order to find the largest two digit number that divides 673 and 865 leaving remainder 1 in each , first subtract 1 from both, then find HCF of both,

➡️673 - 1 = 672

➡️865 - 1 = 864

 

Now,

Finding out their HCF :-

➡️ 672 = 2 × 2 × 2 × 2 × 2 × 3 × 7

➡️ 864 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3

So,

HCF = 2 × 2 × 2 × 2 × 2 × 3

➡️96

Hence,

The largest number which divides 673 and 856 leaving remainder 1 is "96".