Question

Find the greatest number which will divide 625 and 1433 leaving remainders 5
and 3 respectively. ​

Answer 1

The required number is 10.

Step-by-step explanation:

Each time when the number divides 625 and 1433 it leaves remainder 5 and 3 respectively.

So, the number exactly divides (625 - 5) and (1433 - 3) ⇒ the number divides 620 and 1430

So, the required number which when divides 625 and 1433 and leaves remainder 5 and 3 respectively will be HCF (620, 1430)

Now, to find HCF (620, 1430) : Find the prime factors of 620 and 1430

620 = 2 × 2 × 5 × 31

1430 = 2 × 5 × 11 × 13

So, we can see the common factor in both the numbers are 2 and 5

⇒ HCF = 2 × 5 = 10

So, the greatest number which when divides 625 and 1433 leaves remainder 5 and 3 respectively will be 10.

Answer 2

Step-by-step explanation:

Each time when the number divides 625 and 1433 it leaves remainder 5 and 3 respectively. So, the greatest number which when divides 625 and 1433 leaves remainder 5 and 3 respectively will be 10.