Question

find the largest number which divide 1280 and 1371 leaving remainder 7 in each case

Answer 1

In dividing both no we need reminder 7 .
We have to find HCF of (1280-7) and (1371-7)
Hope you can solve further.

Answer 2

Answer:

The required number is 1.

Step-by-step explanation:

Each time when the number divides 1280 and 1371 it leaves remainder 7 in each case.

So, the number exactly divides (1280 - 7) and (1371 - 7) ⇒ the number divides 1273 and 1364

So, the required number which when divides 1280 and 1371 and leaves remainder 7 in each case will be HCF (1273, 1364)

Now, to find HCF (1273, 1364) : Find the prime factors of 1273 and 1364

1273 = 19 × 67

1364 = 2 × 2 × 11 × 31

So, we can see there are no common factor in both the numbers

⇒ HCF = 1

So, the greatest number which when divides 1280 and 1371 leaves remainder 7 in each case is 1.