Question

find the greatest number which divides 1051 and 1525 leaving remainder 6 and 5 respectively

Answer 1

1051 -6= 1045
1525 -5=1520

now find HCF of 1045 and 1520

Answer 2

Answer:

The required number is 98.

Step-by-step explanation:

Each time when the number divides 1051 and 1525 it leaves remainder 6 and 5 respectively.

So, the number exactly divides (1051 - 6) and (1525 - 5) ⇒ the number divides 1045 and 1520

So, the required number which when divides 1051 and 1525 and leaves remainder 6 and 5 respectively will be HCF (1045, 1520)

Now, to find HCF (1045, 1520) : Find the prime factors of 1045 and 1520

1045 = 5 × 11 × 19

2788 = 2 × 2 × 2 × 2 × 5 × 19

So, we can see the common factor in both the numbers are 5, 19

⇒ HCF = 5 × 19 = 95

So, the greatest number which when divides 1051 and 1525 leaves remainder 6 and 5 respectively will be 95.