How to Tell If a Number Is Prime or Composite
Learn how to list factors and multiples, find common factors and multiples, and classify numbers as prime or composite. Master key skills from Chapter 5.
How do you know if a number is prime or composite?
A number is prime if it has exactly two factors: 1 and itself; it is composite if it has more than two factors. In CBSE Class 6 Mathematics Chapter 5, you learn to list all the factors of a number, find common factors and multiples, and classify numbers up to 100 as prime or composite. This article also covers how to identify co-prime pairs, twin primes, and the special case of the number 1. These are essential concepts for building a strong foundation in number theory.
How do you list all factors and multiples of a number?
To list all the factors of a number, you find all whole numbers that divide it exactly without leaving a remainder. Factors are always less than or equal to the number. Multiples of a number are what you get when you multiply that number by 1, 2, 3, and so on. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, because each divides 12 exactly. The first five multiples of 7 are 7, 14, 21, 28, and 35. Factors are limited, but multiples go on forever. A common mistake is to confuse factors with multiples; remember, factors divide the number, while multiples are obtained by multiplying the number.
How do you find common factors and common multiples?
Common factors are numbers that divide two or more numbers exactly. To find them, list the factors of each number and pick the ones they share. The highest common factor (HCF) is the largest of these. Common multiples are numbers that are multiples of two or more numbers; the smallest common multiple (LCM) is the least of these. For example, for 8 and 12, the factors are: 8: 1, 2, 4, 8; 12: 1, 2, 3, 4, 6, 12. Common factors: 1, 2, 4. HCF: 4. The first few multiples of 3 and 4 are: 3: 3, 6, 9, 12, 15, 18; 4: 4, 8, 12, 16, 20. Common multiples: 12, 24, etc. LCM: 12. Sometimes students mix up HCF and LCM; HCF is about dividing, LCM is about multiplying.
How do you tell if a number up to 100 is prime or composite?
A number up to 100 is prime if it has exactly two distinct factors: 1 and itself. If it has more than two factors, it is composite. To check, count how many numbers divide it exactly. For example, 17 is prime because only 1 and 17 divide it exactly. 18 is composite because it has factors 1, 2, 3, 6, 9, and 18. The number 1 is special: it has only one factor (itself), so it is neither prime nor composite. Many students forget that 2 is the only even prime number; all other even numbers are composite.
What are twin primes and co-prime numbers?
Twin primes are pairs of prime numbers that differ by 2, like (3, 5) or (11, 13). Co-prime numbers are two numbers whose only common factor is 1, even if neither is prime. For example, 8 and 15 are co-prime because their only common factor is 1, even though both are composite. In real life, if you have 8 laddus and 15 students, you cannot divide them equally among more than one student, showing they are co-prime. Students often think co-primes must be prime numbers, but this is not true—any two numbers with only 1 as a common factor are co-prime.
Exam tip
The mistake most students make with factors and multiples
Students often confuse factors and multiples. For example, they may say 12 is a factor of 3, but actually, 3 is a factor of 12. The correct way: factors are numbers that divide a given number exactly (e.g., 3 is a factor of 12), while multiples are what you get by multiplying the number (e.g., 12 is a multiple of 3). Remember: factors are smaller or equal, multiples are greater or equal.
Did you know
Why is 2 the only even prime number?
2 is the only even prime number because every other even number can be divided by 2 and at least one other number, making them composite. All other even numbers have at least three factors: 1, 2, and the number itself. This makes 2 unique among primes.
Key takeaways
Prime and composite numbers in 30 seconds
- List all factors by checking which numbers divide a given number exactly.
- Find common factors and multiples by listing them out and identifying shared ones; HCF is the largest common factor, LCM is the smallest common multiple.
- Classify numbers up to 100 as prime (two factors) or composite (more than two); 1 is neither.
- Twin primes differ by 2; co-primes have only 1 as a common factor, even if neither is prime.
Try classifying a few numbers yourself and see how quickly you can spot primes and co-primes!
- Find common factors and multiples by listing them out and identifying shared ones; HCF is the largest common factor, LCM is the smallest common multiple.
- Classify numbers up to 100 as prime (two factors) or composite (more than two); 1 is neither.
- Twin primes differ by 2; co-primes have only 1 as a common factor, even if neither is prime.
Try classifying a few numbers yourself and see how quickly you can spot primes and co-primes!