Prime numbers
Know and use the vocabulary of prime numbers, prime factors, and composite numbers; establish whether a number up to 100 is prime; recall prime numbers up to 19
What a learner can do afterwards
- Explain that a prime number has exactly two factors: 1 and itself
- Determine whether 51 is prime or composite and justify the answer
- List all prime numbers up to 19 from memory
1 · Read
You already know a factor is a number that divides exactly into another number, with nothing left over. A composite number has three or more factors. A prime number is stricter: it has exactly two factors, 1 and itself. That is why 1 is not prime, it only has one factor, itself.
Is 51 prime or composite? Try dividing by small primes. 51 divided by 3 is 17 exactly, with nothing left over. So 51 has the factors 1, 3, 17, and 51, four factors in total. That is more than two, so 51 is composite.
To test any number up to 100, you only need to try dividing it by 2, 3, 5, and 7. If none of those divide it exactly, the number is prime.
A prime number has exactly two factors, 1 and itself, and you can test any number up to 100 by checking a few small primes.
More to read
Prime and composite numbers review
A prime number is a number that has exactly two factors: 1 and itself. Take the number 7. The only numbers that divide evenly into 7 are 1 and 7, so 7 is prime. A composite number has more than two factors. For example, 12 is composite because you can divide it evenly by 1, 2, 3, 4, 6, and 12. To check if a number is prime, try dividing it by small numbers like 2, 3, 5, and 7. If nothing divides evenly except 1 and the number itself, it is prime!
Prime and composite numbers intro
Factors are whole numbers that divide evenly into another number, with nothing left over. The number 15 has four factors: 1, 3, 5, and 15, because each one divides into 15 evenly. Every number has 1 and itself as factors. Numbers get sorted into two groups. A number with exactly two factors, 1 and itself, is called prime. A number with more than two factors is called composite. The number 1 is special: it only has one factor, so it is neither prime nor composite.
Find Multiples and Factors
To find all the factors of a number, try dividing it by 1, 2, 3, and so on, and see which ones work evenly. Some quick tricks help: a number is divisible by 2 if it ends in 0, 2, 4, 6, or 8. It's divisible by 5 if it ends in 0 or 5. Once you have a full list of factors, count them. If there are exactly two factors, the number is prime. If there are more than two, it's composite. For example, 29 only has 1 and 29 as factors, so it's prime. But 51 has 1, 3, 17, and 51, so it's composite.
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18 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.