### Number Theory Quiz #1

Question 1

Find the H.C.F of:

12, 24, 60

**Solution:**

Factors of 12 = {1, 2, 3, 4, 6, 12}

Factors of 24 = {1, 2, 3, 4, 6, 8, 12, 24}

Factors of 60 = {1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60}

Therefore, the H.C.F. = 12

Question 2

Find the inverse of:

(a) 10

Under addition.

(b) -5

Under multiplication.

**Solutions:**

(a)

The inverse of 10:

10 + x = 0

x = -10

i.e. the inverse is, -10.

(b)

The inverse of -5:

Question 3

Write an identity that summarizes the:

(i) Associative law (addition).

(ii) Commutative law (multiplication).

(iii) Distributive law.

**Solutions:**

(i)

(a + b) + c = a + (b + c)

Recall, the Associative law states that the sum/product obtained in an addition/multiplication is not dependent on how the numbers are grouped.

(ii)

a x b = b x a

Recall, the Commutative law states that numbers can be swapped and the sum/product remains the same in an addition/multiplication.

(iii)

(a + b) x c = a x c + b x c