krit.club logo

Prime Time - Prime Numbers

Grade 6CBSE

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

🔑Concepts

•

A Prime Number is a natural number greater than 11 that has exactly two factors: 11 and the number itself. Examples include 2,3,5,7,11,13,17,19,…2, 3, 5, 7, 11, 13, 17, 19, \dots

•

A Composite Number is a natural number that has more than two factors. Examples include 4,6,8,9,10,12,…4, 6, 8, 9, 10, 12, \dots

•

The number 11 is a unique number as it has only one factor (itself). Therefore, 11 is neither prime nor composite.

•

22 is the smallest prime number and it is the only even prime number. All other prime numbers are odd.

•

Twin Primes are pairs of prime numbers that have a difference of 22. Examples: (3,5)(3, 5), (5,7)(5, 7), (11,13)(11, 13), and (17,19)(17, 19).

•

Co-prime Numbers are two numbers that have only 11 as their common factor. They do not necessarily have to be prime themselves. For example, 88 and 1515 are co-prime because their only common factor is 11.

•

Prime Factorization is the process of expressing a composite number as a product of its prime factors. For example, 12=2×2×3=22×312 = 2 \times 2 \times 3 = 2^2 \times 3.

📐Formulae

Factors of a Prime Number p={1,p}\text{Factors of a Prime Number } p = \{1, p\}

A number n>1 is composite if factors of n>2\text{A number } n > 1 \text{ is composite if factors of } n > 2

General Prime Factorization: N=p1a×p2b×p3c…\text{General Prime Factorization: } N = p_1^{a} \times p_2^{b} \times p_3^{c} \dots

Twin Primes condition: ∣p1−p2∣=2\text{Twin Primes condition: } |p_1 - p_2| = 2

💡Examples

Problem 1:

Check whether 2929 is a prime number or a composite number.

Solution:

Prime Number

Explanation:

To check if 2929 is prime, we find its factors. The factors of 2929 are 11 and 2929 because it cannot be divided by any other prime numbers like 2,3,5,…2, 3, 5, \dots without leaving a remainder. Since it has exactly two factors, it is a prime number.

Problem 2:

Find the prime factorization of 9090.

Solution:

90=2×3×3×5=2×32×590 = 2 \times 3 \times 3 \times 5 = 2 \times 3^2 \times 5

Explanation:

We divide 9090 by the smallest prime number possible: 90÷2=4545÷3=1515÷3=55÷5=1\begin{array}{r} 90 \div 2 = 45 \\ 45 \div 3 = 15 \\ 15 \div 3 = 5 \\ 5 \div 5 = 1 \end{array} So, the prime factors are 2,3,3,2, 3, 3, and 55.

Problem 3:

Are 1515 and 1616 co-prime numbers?

Solution:

Yes, they are co-prime.

Explanation:

First, we find the factors of both numbers: Factors of 1515: 1,3,5,151, 3, 5, 15 Factors of 1616: 1,2,4,8,161, 2, 4, 8, 16 The only common factor between 1515 and 1616 is 11. Since the Highest Common Factor (HCF) is 11, they are co-prime.