Question

find the greatest number that will divide 143,67 and 89 leaving remainders 3,7 and 4 respectively.

Answer 1

The greatest number
= hcf of (143-3), (67-7), (89-4)
= hcf of 140, 60, 85
= 5

Answer 2

Answer:

The required number is 5.

Step-by-step explanation:

Each time when the number divides 143, 67 and 89 it leaves remainder 3, 7 and 4 respectively.

So, the number exactly divides (143 - 3), (67 - 7) and (89 - 4) ⇒ the number divides 140, 60 and 85

So, the required number which when divides 143, 67 and 89 and leaves remainder 3, 7 and 4 respectively will be HCF (140, 60, 85)

Now, to find HCF (140, 60, 85) : Find the prime factors of 140, 60 and 85

140 = 2 × 2 × 5 × 7

60 = 2 × 2 × 3 × 5

85 = 5 × 17

So, we can see the common factor in all the numbers is 5

⇒ HCF = 5

So, the greatest number which when divides 143, 67 and 89 leaves remainder 3, 7 and 4 respectively will be 5.