Properties of Integers

Question 1

Find the least number which leaves the remainder 5 when divided by 8,12,16 and 20.

Answer 1

245

Question 2

If f(n) = n(n-1), then f(6)

Answer 2

30

Question 3

If an = (1 + 3n)2 (–1)n , then a3

Answer 3

-100

Question 4

If n is an integer, then n(n-1)(2n-1) is divisible by

Answer 4

6, given first that n is 1 and then 2 … then show than the results are divisible by 6

Question 5

Find number of positive divisors of 1420

Answer 5

12

Question 6

Two numbers are in ratio 3:4, if their LCM is 240, the smaller of two number is

Answer 6

60

Question 7

How many different factors does 24 have including 1 and 24?

Answer 7

8

Question 8

Fundamental theorem of arithmetic: every positive integer n > 1 can be written uniquely as a product of:

Answer 8

prime

Question 9

Distance between the integers – 4 and 2

Answer 9

6

Question 10

Two integers a and b are said to be relatively prime or coprime if

Answer 10

gcd(a,b) =1

Question 11

If (a, 4) =2 and (b, 4) = 2, then (a+b, 4)

Answer 11

4

Question 12

The LCM of (26, 195) =

Answer 12

390 that is mulitply the two mulitples and divide the result by the addition of the a and b

Question 13

Evaluate: |2 – 5| +|3 -6| =

Answer 13

6. Where the bars represent the absolute value, which is always the a positive.

Question 14

|a ± b| ≤_______ ?

Answer 14

|a| +|b|