Question

2. The largest number which divides 70 and 125, leaving remainders 5 and 8 respectively
is?
​

Answer 1

Answer:

13

Step-by-step explanation:

Largest no. divides 70 and 125 leaving remainders 5 and 125

So let's find the numbers which are exactly divisible

As they leave 5 and 8 remainders. No. which are exactly divisible :

• 70 - 5 = 65
• 125 - 8 = 117

The largest no. which divides 70 and 125 leaving 5 and 8 remainders would be the HCF of 65 and 117

Using Euclid division algorithm a = bq + r, where 0 < or = r < b

117 = 65 × 1 + 52

65 = 52 × 1 + 13

52 = 13 × 4 + 0

Since remainder is 0 the divisor i.e ' b ' at this stage is HCF

HCF of 117 and 65 = 13

Therefore the largest number which divides 70 and 125, leaving remainders 5 and 8 respectively is 13.