Unit 3 Contents

Check-In: Question 3

3. Use factor trees to factor each of the following numbers into primes. Write number sentences to show your answers.
1. 18
2. 12
3. 56
4. 90

1. Find all the factors of 18.
2. How does your answer compare to your answer for Question 3A?
3. Are all the factors of 18 also prime factors of 18?
4. Are all the prime factors of 18 also factors of 18?

Prime Factors and Exponents

Lee Yah factored 45 into prime factors. She wrote 45 = 5 3 3. Linda found the same prime factors of 45 but wrote them using an exponent: 45 = 5 3².

5. Write your answers to Questions 3A–D using exponents.
6. Find the prime factorization of each of the following numbers. Write your answers using exponents.
1. 100
2. 40
3. 80
4. 500

Number Riddles

Show or tell how you solve each of these riddles.

7. I am a prime number between 10 and 20. I am one more than a square number.
   What number am I?
8. I am a multiple of 3. I am a square number. I am less than 20. What number am I?
9. I am a multiple of 5. Two is not one of my factors. I am not prime and I am not square.
   I am less than 30. What number am I?

Did You Know?
Some mathematicians study ways to factor large numbers. This is part of a branch of mathematics called number theory. Mathematicians study number theory because it is fun and interesting. Many of the discoveries that mathematicians made about number theory later turned out to be very useful. For example, factoring is important in making and breaking secret codes.