In a previous lesson, students learned that 1 is a factor of any number. In this lesson, they use that knowledge to learn the definition of a prime number.
A prime number is defined as any number greater than 1 whose only factors are 1 and the number itself.
Numbers that are not prime are fractions, the number 0, 1, and any number that has a factor other than 1 and the number itself.
In this lesson, students learn that a composite number is a number that has more than the two factors 1 and the number itself.
Thus composite numbers include all non-prime numbers except 1 and 0.
All composite numbers can be expressed as the product of prime numbers. These are called prime factors. The prime factorization of a number is the set of all prime factors.
In this lesson, students learn to write the prime factorization of composite numbers up to 50. They learn to use a systematic strategy that is based on starting with 2, the smallest prime number, then trying the next three largest prime numbers in succession – 3, 5, and 7. These are all the prime factors of numbers less than 50.
In completing the prime factorization, students must show their work by entering on screen all the prime factors identified for a given number using the strategy above.
They must then write the prime factorization from this list of all possible prime factors, using each prime number.
In this lesson, students extend what they learned about identifying prime factors of a number in the prior lesson to write the prime factorization of that number.
They start by identifying all the prime factors of a given number using the strategy learned in the prior lesson.
They then write the prime factorization by taking each of the prime factors identified and writing them as a multiplication statement whose product is the original number.