Lesson 2: Breaking Down Numbers. Prime Factors
Lesson 2: Breaking Down Numbers. Prime Factors
Prime factorization, greatest common factor and least common multiple.
Numbers can be broken down into smaller numbers or themselves and 1.
Prime factors are numbers that cannot be split further into other whole numbers, other than themselves and 1.
Factors in general are numbers that the given number can be divided by. Or whole numbers that are multiplied together to produce another number. The original numbers are factors of the product. If a x b = c then a and b are factors of c.
For example, the factors of 8 are 1, 8, 2, 4.
In this lesson we are learning about prime factors, how to determine them and why we need them.
We are also discussing the concept of the Greatest Common Factor for the given two numbers. The GCF is the largest number the two given numbers could be divided by.
The Least Common Multiple is the smallest number that could be divided by the given two numbers.
For example, the LCM of 4 and 8 is 8, because it could be divided by both 4 and 8 and it is the lowest possible value.
LCM will later be used to determine the Lowest Common Denominator of the two fractions.
Its extremely important to understand the concepts studies in this lesson and learn all of the different methods of breaking down natural numbers. These concepts are the foundation for some of the more complex topics.
Key ideas: Breaking Down Numbers. Prime Factors
A prime number has exactly two factors: 1 and itself (2, 3, 5, 7, 11, …). Every whole number greater than 1 can be written as a product of primes, its prime factorization. A factor tree helps find it.
- Greatest Common Factor (GCF): the biggest number that divides both numbers. Use it to simplify fractions or split things into equal groups.
- Lowest Common Multiple (LCM): the smallest number that both numbers divide into. Use it to find common denominators or when things “line up” again.
Worked examples
Example 1
Find the prime factorization of 60.
- 60 = 6 × 10 = (2 × 3) × (2 × 5).
- 60 = 2 × 2 × 3 × 5
Example 2
Find the GCF of 36 and 48.
- 36 = 2 × 2 × 3 × 3 and 48 = 2 × 2 × 2 × 2 × 3.
- Shared factors: 2 × 2 × 3 = 12
Example 3
Find the LCM of 6 and 8.
- Multiples of 8: 8, 16, 24, … Which is also a multiple of 6? 24.
- LCM = 24
Example 4
Hot dogs come in packs of 10 and buns in packs of 8. What is the smallest number of each pack to have the same number of hot dogs and buns?
- LCM of 10 and 8 is 40.
- 40 ÷ 10 = 4 packs of hot dogs and 40 ÷ 8 = 5 packs of buns.
Common mistakes
- Calling 1 a prime number (it is not).
- Mixing up GCF and LCM: the GCF is never bigger than the smaller number; the LCM is never smaller than the bigger number.
Questions students ask
Is 2 a prime number?
Yes. It is the only even prime number.
Breaking Down Numbers and Prime Factors Quiz
Check your understanding
Try the quiz for this lesson. You’ll see right away if each answer is correct.