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### Greatest Common Divisor

• Greatest Common Divisor (GCD) is also known as Greatest Common Factor (GCF). The Greatest Common Divisor of two or more numbers is the largest factor shared by all the numbers.
• You can find the GCD by listing factors. If you do this, make sure you put the factors for each number in pairs to avoid omitting a number.
• For example: 12: 1 • 12, 2 • 6, 3 • 4; then put the factors in ascending order 12: 1, 2, 3, 4, 6, 12
• You can find the GCD by using Prime Factorization.
• Steps to Using Prime Factorization to Find GCD:
1. Make the factor tree for each number
2. Circle each factor that the numbers have in common
3. Take only one set of circled factors and multiply

### Greatest Common Divisor

Find the Greatest Common Divisor (GCD) of 48 and 60 by listing their divisors.
• 48: 1, 2, 3, 4, 6, 8, 12, 24, 48
• 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
• Common divisors: 1, 2, 3, 4, 6, 12
GCD: 12
Find the GCD of 80 and 125 by listing their divisors.
• 80: 1, 2, 3, 4, 5, 8, 10, 16, 20, 40, 80
• 125: 1, 5, 15, 125
• Common divisors: 1, 5
GCD: 5
Find the GCD of 75 and 125 by listing their divisors.
• 75:1, 3, 5, 15, 25, 75
• 125: 1, 5, 25, 125
• Common divisors: 1, 5, 25
GCD: 25
Find the GCD of 52 and 78 by listing their divisors.
• 52: 1, 2, 4, 13, 26, 52
• 78: 1, 2, 3, 6, 13, 26, 39, 78
• Common divisors: 1, 2, 13, 26
GCD: 26
Find the GCD of 45 and 63 by using prime factorization.
• 45 =
5 ·9 =
5 ·3 ·3 =
32 ·5
• 63 =
7 ·9 =
7 ·3 ·3 =
32 ·7
• Common factors: 3 ·3
GCD: 9
Find the GCD of 18 and 24 by using prime factorization.
• 18 =
3 ·6 =
3 ·2 ·3 =
2 ·32
• 24 =
3 ·8 =
3 ·2 ·4 =
3 ·2 ·2 ·2 =
22 ·3
• Common factors: 2 ·3
GCD: 6
Find the GCD of 66 and 242 by using prime factorization.
• 66 =
6 ·11 =
2 ·3 ·11
• 242 =
2 ·121 =
2 ·11 ·11 =
2 ·112
• Common factors: 2 ·11
GCD: 22
Find the GCD of 36, 54, and 72 by listing divisors.
• 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
54: 1, 2, 3, 6, 9, 18, 27, 54
72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 36, 72
• Common divisors: 1, 2, 3, 6, 9, 18
GCD: 18
Find the GCD of 15, 30, and 65 by using prime factorization.
• 15 =
3 ·5
• 30 =
3 ·10 =
2 ·3 ·5
• 65 =
5 ·13
• Common factor: 5
GCD: 5
A rabbit has three carrots measuring 16, 24, and 32 inches. She wants to cut these carrots into as many equal pieces as possible without wasting any material. How long should each piece be cut into? List divisors to solve this proble.
• 16: 1, 2, 4, 8, 16
24: 1, 2, 3, 4, 6, 8, 12, 24
32: 1, 2, 4, 8, 16, 32
• Common divisors: 1, 2, 4, 8
GCD: 8
8 inches

*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.

### Greatest Common Divisor

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 0:07
• Topics Overview
• Vocabulary 0:41
• Factor
• Common Divisor
• Greatest Common Divisor (GCD)/ Greatest Common Factor (GCF)
• Find the GCD by Listing Divisors 1:34
• GCD of 27 and 36
• GCD of 18 and 49
• Prime Factorization to Find GCD 3:30
• GCD of 42 and 72
• GCD of 21 and 63
• GCD in Word Problems 5:30
• Greatest Number of Police Officers
• GCD in Word Problems 7:15
• Cutting Two Pipes
• Extra Example 1: GCD of 32, -24, 40 8:08
• Extra Example 2: How Many Groups? 9:41
• Extra Example 3: GCD of Two Prime Numbers 11:34
• Extra Example 4: How Many Children? 12:26