Virginia Standard Breakdown

5.NS.2 – Understanding Prime and Composite Numbers

Students will learn to identify prime and composite numbers up to 100, explain their reasoning, and break numbers up into the prime numbers that make them.

When will I ever use this?

You will use prime and composite numbers any time you need to split things into equal groups, find patterns, or make things fair. And prime factorization is used in jobs like coding, building, baking, and even music — because it’s all about breaking big things into smaller, basic parts.

Jobs that Use Prime Factorization

• Electricians – use factors to figure out circuits and how much power can be shared.

• Musicians / Sound Engineers – prime factors connect to rhythms and sound waves (beats, patterns, vibrations).

• Carpenters & Builders – use factors to cut materials evenly or measure spaces correctly.

• Chefs / Bakers – use factorization when scaling recipes up or down for big groups.

• Computer Scientists – use prime factorization to keep information safe (passwords, banking, online shopping).

Terms to know

• Factor: a number that can be divided evenly into another number

• Prime Number: a number with exactly two factors (1 and the number itself) 

• Composite number: a number with more than 2 factors

• Prime Factorization:  when you break a number down into only prime numbers that multiply together to make the original number.

Examples: 

• Prime numbers have only two factors: 1 and itself. Example: 7 → 1,7
  
  

• Composite numbers have more than two factors. Example: 12 → 1, 2, 3, 4, 6, 12

What numbers your should automatically know are composite?

• ALL even numbers (except for 2) are composite

  • WHY? All even numbers can be divided by 2, so they have more than two factors 

• ALL numbers that end in a zero OR 5 (except for 5) are composite

  • WHY? All numbers ending in 0 or 5 can be divided by 5, so they have more than two factors -- except 5, which only has 1 and 5.

• ALL double numbers (22, 33, 44 etc.) (except for 11) are composite

  •  WHY? All double numbers can all be divided by 11, so they have more than two factors -- except 11, which only has 1 and 11. 

**This means, you should easily be able to figure out 61 of the numbers between 2 and 100! **

What if I can't figure out the number automatically?

• If you can't figure out off the top of your head without knowing if the given number is prime or composite, you can use the Prime box. 

• If the number in question divides evenly (no decimals) by all numbers in the prime box, the number is composite. If all answers come out as a decimal, the number is prime! 

• ALSO - if a number is in the prime box (2,3,5,7) it's prime.

Prime Factorization

What is Prime Factorization? 

• Prime factorization is when you break a number down into only prime numbers that multiply together to make the original number.

What are the steps for finding the prime factorization?

• Start with a number at the top

• Find two numbers that multiply to make it.

• If one of those numbers is prime, circle it. If it’s not, keep breaking it down.

• Keep going until all the numbers are prime.

• The circled numbers are the prime factors.