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4. Match the items in column I with the items in column II.

Column I Column II

(a) Common factors of 6 and 8 (i) 18
(b) Common factors of 16 and 20 (ii) 20 and 40
(c) Common multiples of 6 and 9 less than 30 (iii) 1 and 2

(d) Common multiples of 4 and 10 less 50 (iv) 1, 2 and 4

5. Find the two numbers whose product is 24 and difference is 2.
6. Look at the table below and answer the following: (NCERT) 31 32 33 34 35 36 37 38 39 40
(a) Is there anything common among the shaded numbers? 41 42 43 44 45 46 47 48 49 50
(b) Is there anything common among the circled numbers? 51 52 53 54 55 56 57 58 59 60
(c) Which numbers are both shaded and circled? Is there 61 62 63 64 65 66 67 68 69 70
anything common among these numbers?
7. Find the HCF and LCM of the following numbers. Verify that the product of the numbers is the same
as the product of their HCF and LCM.
(a) 28 and 44 (b) 52 and 143

5.3 PRIME AND COMPOSITE NUMBERS

Prime Numbers

A prime number is a number which has only two factors, 1 and the number itself. This means a prime number
can be completely divided only by 1 or itself. It must be a whole number greater than 1.
For example: The number 7 can only be divided exactly by 1 or 7, therefore, it is a prime number. Similarly,
2, 3, 5, 11, 13, etc. are prime numbers.
So, the numbers greater than 1, whose only factors are 1 and the number itself are called prime numbers.

Composite Numbers

A composite number is a number which has more than two factors. That is, it can be completely divided by
numbers other than 1 or itself.

Algorithm to Find if a Number is Prime or Composite

Step 1: Find all factors of the number.
Step 2: If the number has only two factors, one and itself, then it is prime.

Step 3: If the number has more than two factors, then it is composite.
Ex. Determine whether the given two numbers are
prime or composite: (a) 36 (b) 17. Remember
Sol. (a) Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36. 1. 0 is neither a prime nor a composite number.
It has more than two factors. So, 36 is a 2. 1 is neither a prime nor a composite number.
composite number. 3. All whole numbers other than zero and one
are either composite or prime.
(b) Factors of 17 = 1, 17. It has only two factors. 4. The natural number 2 is the smallest and
So, 17 is a prime number. the only even prime number.

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