Question

Find the largest number which divides 149 and 101 , leaving remainder of 5

Answer 1

149-5=144
101-5=96
HCF of 96 and 144 =48 is the largest required number.

Answer 2

48 is greatest number which divides both number 149 and 101 and leaving remainder 5.

Solution:

Let us take two numbers as N and M

N = 149 – 5 = 144

M = 101 – 5  = 96

Now subtracting 5 from the number we get 144 and 96.

Now to find largest number which divides both the number and to leave remainder 5 , HCF can be used.

Using factorization method we get  

$\begin{array}{l}{144=2 \times 2 \times 2 \times 2 \times 3 \times 3} \\ {96=2 \times 2 \times 2 \times 2 \times 2 \times 3}\end{array}$

Common factors are $\bold{2 \times 2 \times 2 \times 2 \times 3=48}$