Teaching Notes 1.10: Writing Prime Factorization
Expressing a composite number as a product of its prime factors is called writing the prime
factorization. A common error students make is failing to complete the prime factorization of a
number by mistaking a composite number for a prime.- Make sure your students understand the definition of a prime number. A prime number is a
whole number greater than 1 that has only two factors: 1 and itself. Compare this definition
with that of a composite number: a whole number greater than 1 that has more than two
factors. Note that 1 is neither prime nor composite. - Point out the first ten prime numbers on the worksheet. Ask your students to volunteer
examples of composite as well as other prime numbers. - Explain that every composite number can be uniquely expressed as the product of prime
factors. The order of the prime factors does not matter. 15= 3 ×5or5×3. - Review the information and example on the worksheet with your students. Note that all
of the factors in prime factorization are prime numbers and that the factors are written
in ascending order. Also note how the prime factors can be written with exponents. For
example, the prime factorization of 20 can be written as 2× 2 ×5or2^2 ×5.
EXTRA HELP:
2 is a prime factor of every even number.ANSWER KEY:
(1) 2 × 5 × 7 (2) 22 × 7 (3) 22 × 3 × 5 (4) 22 × 52 (5) 34 (6) 32 × 5
(7) 3 × 52 (8) 23 × 3 (9) 22 × 3 × 52 (10) 2 × 32 × 7
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(Challenge) 6 = 2 ×3. 2 and 3 are the two smallest prime numbers.
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