List all the factors of each number. Then, find the common factors and the greatest common factor of each number: 1. 15 = 20 = GCF= 2. 16 = 20 = GCF= 3. 12 8 GCF= 4. 17 = 51 = GCF= 5. 36 = 42 = GCF= 6. 32= 40= GCF= 7. 9= 21= GCF= 8. 36= 42= GCF= 9. 16= 56= GCF= 10. 21= 30= GCF=
The Correct Answer and Explanation is:
You said:
List all the factors of each number. Then, find the common factors and the greatest common factor of each number: 1. 15 = 20 = GCF= 2. 16 = 20 = GCF= 3. 12 8 GCF= 4. 17 = 51 = GCF= 5. 36 = 42 = GCF= 6. 32= 40= GCF= 7. 9= 21= GCF= 8. 36= 42= GCF= 9. 16= 56= GCF= 10. 21= 30= GCF=without using the em dashes,PROVIDE the correct answer and 300 words explanation
ChatGPT said:
To solve this problem, we first list the factors of each number, then identify the common factors between each pair of numbers. Finally, we determine the greatest common factor (GCF), which is the largest number that divides both numbers in each pair.
1. 15 and 20
- Factors of 15: 1, 3, 5, 15
- Factors of 20: 1, 2, 4, 5, 10, 20
- Common factors: 1, 5
- GCF: 5
2. 16 and 20
- Factors of 16: 1, 2, 4, 8, 16
- Factors of 20: 1, 2, 4, 5, 10, 20
- Common factors: 1, 2, 4
- GCF: 4
3. 12 and 8
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 8: 1, 2, 4, 8
- Common factors: 1, 2, 4
- GCF: 4
4. 17 and 51
- Factors of 17: 1, 17
- Factors of 51: 1, 3, 17, 51
- Common factors: 1, 17
- GCF: 17
5. 36 and 42
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
- Common factors: 1, 2, 3, 6
- GCF: 6
6. 32 and 40
- Factors of 32: 1, 2, 4, 8, 16, 32
- Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
- Common factors: 1, 2, 4, 8
- GCF: 8
7. 9 and 21
- Factors of 9: 1, 3, 9
- Factors of 21: 1, 3, 7, 21
- Common factors: 1, 3
- GCF: 3
8. 36 and 42
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
- Common factors: 1, 2, 3, 6
- GCF: 6
9. 16 and 56
- Factors of 16: 1, 2, 4, 8, 16
- Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
- Common factors: 1, 2, 4, 8
- GCF: 8
10. 21 and 30
- Factors of 21: 1, 3, 7, 21
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- Common factors: 1, 3
- GCF: 3
Explanation:
To find the greatest common factor (GCF) of two numbers, you first list all their factors. The factors of a number are all the numbers that divide it evenly. After listing the factors of both numbers, you identify the common factors, which are the numbers that appear in both lists. The largest of these common factors is the GCF. For example, for 15 and 20, the factors of 15 are 1, 3, 5, and 15, while the factors of 20 are 1, 2, 4, 5, 10, and 20. The common factors are 1 and 5, and the greatest common factor is 5.
This process applies to each pair of numbers. Identifying the GCF helps simplify fractions, find equivalent fractions, and solve problems in number theory.
