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Prime and Composite Numbers - basics

Grade 4CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A factor is a number that divides another number exactly, leaving a remainder of 00.

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Prime Numbers: A number greater than 11 that has exactly two factors: 11 and the number itself. Examples: 2,3,5,7,112, 3, 5, 7, 11.

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Composite Numbers: A number that has more than two factors. Examples: 4,6,8,9,10,124, 6, 8, 9, 10, 12.

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The number 11 is unique; it has only one factor (11), so it is neither prime nor composite.

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The number 22 is the smallest prime number and the only even prime number. All other even numbers are composite because they have at least 1,2,1, 2, and themselves as factors.

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Every composite number can be written as a product of prime numbers.

📐Formulae

Prime Number Factors={1,number itself}\text{Prime Number Factors} = \{1, \text{number itself}\}

Number of factors of a Prime Number=2\text{Number of factors of a Prime Number} = 2

Number of factors of a Composite Number>2\text{Number of factors of a Composite Number} > 2

💡Examples

Problem 1:

Identify if 1313 is a prime number or a composite number.

Solution:

To determine this, we find the factors of 1313. We try dividing 1313 by numbers starting from 11: 13÷1=1313 \div 1 = 13 13÷2=613 \div 2 = 6 remainder 11 13÷3=413 \div 3 = 4 remainder 11 ... and so on. The only numbers that divide 1313 exactly are 11 and 1313. Factors of 13=1,1313 = 1, 13. Since it has exactly 22 factors, 1313 is a Prime Number.

Explanation:

A prime number is defined as a number having exactly two factors.

Problem 2:

Find the factors of 1212 and state whether it is prime or composite.

Solution:

Find all pairs of numbers that multiply to give 1212: 1×12=121 \times 12 = 12 2×6=122 \times 6 = 12 3×4=123 \times 4 = 12 Factors of 12=1,2,3,4,6,1212 = 1, 2, 3, 4, 6, 12. Since 1212 has 66 factors (which is more than 22), 1212 is a Composite Number.

Explanation:

A composite number has more than two factors.

Problem 3:

Which is the only even prime number? List the first five prime numbers.

Solution:

The only even prime number is 22. The first five prime numbers are: 2,3,5,7,112, 3, 5, 7, 11.

Explanation:

All other even numbers like 4,6,84, 6, 8 are divisible by 22, meaning they have more than two factors.

basics Class 4 Notes & Examples | CBSE Maths