Question

find the greatest number which divides 260, 1314 and 1331 and leaves remainder 5 in each case

Answer 1

In order to find the greatest number which divides 260, 1314 and 1331 and leaves remainder 5 in each case, firstly we have to subtract 5 from the three numbers and then find their HCF.

So after subtraction we get: 255, 1309 and 1326.

Now 255 = 15 x 17

or, 1309 = 17 x 77

or, 1326 = 17 x 78

Now we can see that there are no other common factors apart from 17.

So, 17 is the HCF and it is the greatest number which divides 260, 1314 and 1331 and leaves remainder 5 in each case.

you can verify it also.

Answer 2

Answer:

• hello sizan , in term to find the greatest no. we have to subtract each no by remainder which is 5
• 255=260-5
• 1309=1314-5
• 1326=1331-5

• now we will find prime factors of no. above found
• 255= (17)(15)
• 1309=(17)(7)(11)
• 1326=(17)(4)(17)
• •°• HCF of these no will be 17
• °•°17 is the HCF which is the largest no which divides 260,1314,1331 and leaves remainder 5 in each case