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### Prime Factorization

• Learn the Divisibility Rules. They will be useful in many situations; anywhere from finding prime factorization to working with fractions.
• Divisibility Rules
• You can divide by these following numbers when…
• 2: any even number, a number ending in 0, 2, 4, 6, or 8
• 3: the sum of the digits is divisible by 3
• 4: the last two digits are divisible by 4
• 5: the number ends in 0 or 5
• 6: both 2 and 3 work
• 9: the sum of the digits is divisible by 9
• 10: the number ends in 0
• A factor is a whole number that divides a nonzero whole number with no remainder.
• A prime number is a number greater than 1 with exactly two factors, 1 and itself.
• Remember that before you decide a number is prime; make sure to check if the number is divisible by 3 or 7. For example, 51 and 57 seem to be prime numbers, but are not!
• A composite number is a whole number greater than 1 with more than two factors.
• Prime Factorization represents a composite number written as a product of prime numbers.
• When writing the prime factorization, order the factors in ascending order and use exponents when possible.

### Prime Factorization

Find the prime factorization of 120.
• 120 =
• 12 ·10 =
• 3 ·4 ·2 ·5 =
• 3 ·2 ·2 ·2 ·5 =
23 ·3 ·5
Find the prime factorization of 180.
• 180 =
• 9 ·20 =
• 3 ·3 ·4 ·5 =
• 3 ·3 ·2 ·2 ·5 =
22 ·32 ·5
Find the prime factorization of 225.
• 225 =
• 15 ·15 =
• 3 ·5 ·3 ·5 =
32 ·52
Find the number with the given prime factorization.
24 ·3 ·52
• 2 ·2 ·2 ·2 ·3 ·5 ·5 =
• 16 ·3 ·25 =
• 48 ·25 =
1200
Find the number with the given prime factorization.
23 ·5 ·7 ·11 =
• 8 ·35 ·11 =
• 88 ·35 =
3080
Is the number 87 prime or composite?
• 87 is divisible by 3. We know this because 8 + 7 = 15, and 15 is divisible by 3.
Composite
Is the number 91 prime or composite?
• 91 is not divisible by 2, 3, 4, 5, 6, 8, 9, or 10
• Try dividing 91 by 7, 11, and 13
• 91 ÷7 = 13
91 is divisible by 7 and 13.
• 91 ÷11 ≈ 8.27
91 is not divisible by 11.
Composite
12 girl scouts are marching in a parade. They must form rows of equal numbers of girl scouts. What are the different marching arrangements?
• 12: 1, 2, 3, 4, 6, 12
1 ×12
2 ×6
3 ×4
4 ×3
6 ×2
12 ×1
Michael needs to arrange 15 seats in rows of equal numbers. What are his options of arranging them?
• 15: 1, 3, 5, 15
1 ×15
3 ×5
5 ×3
15 ×1
Find the prime factorization of 924
• 924 =
• 4 ·231 =
• 2 ·2 ·11 ·21 =
• 2 ·2 ·11 ·3 ·7 =
22 ·3 ·7 ·11

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

### Prime Factorization

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

• Intro 0:00
• What You'll Learn and Why 0:06
• Topics Overview
• Vocabulary 0:23
• Factor
• Composite Number
• Vocabulary 1:17
• Prime Number
• Prime Factorization
• Divisibility Rules 2:54
• Divisibility Rules for 2, 3, 4 ,5 ,6, 9 and 10
• Finding Factors 4:56
• Possible Arrangements
• Finding Factors 6:06
• How Many Oranges?
• Prime or Composite 6:43
• Prime or Composite: 48
• Prime or Composite: 53
• Prime or Composite: 57
• Prime Factorization 8:16
• Prime Factorization of 42
• Prime Factorization of 84
• Find the Number 9:23
• Find the Number with the Given Prime Factorization
• Extra Example 1: Prime or Composite 11:04
• Extra Example 2: Prime Factorization of 72 12:23
• Extra Example 3: Marching Arrangements 12:56
• Extra Example 4: Flowers Arrangements 14:50