Page 47 - Maths Skill - 6

Prime Time 45

3. State which of the following numbers are divisible by 2, 4, or 8.

(i) 652 (ii) 4896 (iii) 37780
(iv) 5086 (v) 19334 (vi) 21084
4. In each of the following numbers, replace the sign ‘*’ by the smallest digit to make them divisible by the
given number.
(i) 157* by 2 (ii) 4129* by 3 (iii) 260*2 by 4 (iv) 7158* by 6 (v) 1305* by 10

(vi) 6511*2 by 9 (vii) 637*8 by 8 (viii) 2*7* by 5 (ix) 215*173 by 11
5. Which of the following numbers are prime?

(i) 39 (ii) 193 (iii) 307 (iv) 327
(v) 283 (vi) 129 (vii) 397 (viii) 187
6. Find all the prime numbers required to test as divisors to determine whether or not the following
numbers are prime. Also determine if the number is a prime number.

(i) 137 (ii) 203 (iii) 317 (iv) 407

PRIME FACTORIZATION Fact-o-meter
The process of expressing a number as a product of only prime factors � A factor of a number is
is called prime factorization. said to be a prime factor
Let us factorize 60 in all possible ways as shown below: if it is a prime number.

60 60 60

60
2 30 3 20 5 12

2 15 2 10 4 15 3 4

3 5 2 5 2 2 3 5 2 2

60 = 2 × 2 × 3 × 5 60 = 3 × 2 × 2 × 5 60 = 2 × 2 × 3 × 5 60 = 5 × 3 × 2 × 2

The prime factorization of a given composite number can be carried out in any 60
way but it is unique.
Thus, every composite number can be factorized into prime factors in one and 6 10
only one way irrespective of the order of its factors.
And the process of finding the prime factors of a given composite number in the
above pattern is called factor tree method. 2 3 2 5
Prime factorization can also be done using division method which is illustrated 60 = 2 × 3 × 2 × 5
as follows. 2 60

2 30
3 15
5 5

1 Thus, 60 = 2 × 2 × 3 × 5