For Exercises 16 - 23, list the common factors for each pair of numbers. Then find the greatest common factor for each pair.
16. 18 and 30 17. 9 and 25
18. 60 and 45 19. 23 and 29
20. 49 and 14 21. 140 and 25
22. 142 and 148 23. 84 and 105
To find the common factors for each pair of numbers and then determine the greatest common factor (GCF), we can follow these steps:
16. For the numbers 18 and 30:
- The factors of 18 are 1, 2, 3, 6, 9, and 18.
- The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.
- The common factors for 18 and 30 are 1, 2, 3, and 6.
- The greatest common factor is 6.
17. For the numbers 9 and 25:
- The factors of 9 are 1, 3, and 9.
- The factors of 25 are 1, 5, and 25.
- The common factors for 9 and 25 are 1.
- The greatest common factor is 1.
18. For the numbers 60 and 45:
- The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
- The factors of 45 are 1, 3, 5, 9, 15, and 45.
- The common factors for 60 and 45 are 1, 3, 5, and 15.
- The greatest common factor is 15.
19. For the numbers 23 and 29:
- The factors of 23 are 1 and 23.
- The factors of 29 are 1 and 29.
- The common factors for 23 and 29 are 1.
- The greatest common factor is 1.
20. For the numbers 49 and 14:
- The factors of 49 are 1, 7, and 49.
- The factors of 14 are 1, 2, 7, and 14.
- The common factor for 49 and 14 is 7.
- The greatest common factor is 7.
21. For the numbers 140 and 25:
- The factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, and 140.
- The factors of 25 are 1, 5, and 25.
- The common factor for 140 and 25 is 5.
- The greatest common factor is 5.
22. For the numbers 142 and 148:
- The factors of 142 are 1, 2, 71, and 142.
- The factors of 148 are 1, 2, 4, 37, 74, and 148.
- The common factors for 142 and 148 are 1 and 2.
- The greatest common factor is 2.
23. For the numbers 84 and 105:
- The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84.
- The factors of 105 are 1, 3, 5, 7, 15, 21, 35, and 105.
- The common factors for 84 and 105 are 1, 3, 7, and 21.
- The greatest common factor is 21.
To find the common factors for each pair of numbers and then determine the greatest common factor, you can start by listing the factors for each number.
For example, let's take the first pair: 18 and 30.
To find the factors of 18, you can start by dividing it by 1. If the division results in a whole number, then 1 is a factor. Next, divide 18 by 2, and so on, until you find all the factors.
Factors of 18: 1, 2, 3, 6, 9, 18
Repeat the same process for the other number, 30.
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Now, looking at the list of factors for both numbers, we can see that the common factors are 1, 2, 3, and 6. To find the greatest common factor, simply choose the largest number from the common factors list, which in this case is 6.
Use the same process to find the common factors and greatest common factors for the other pairs:
16. 18 and 30:
Common factors: 1, 2, 3, 6
Greatest common factor: 6
17. 9 and 25:
Common factors: 1
Greatest common factor: 1
18. 60 and 45:
Common factors: 1, 3, 5, 15
Greatest common factor: 15
19. 23 and 29:
Common factors: 1
Greatest common factor: 1
20. 49 and 14:
Common factors: 1, 7
Greatest common factor: 7
21. 140 and 25:
Common factors: 1, 5
Greatest common factor: 5
22. 142 and 148:
Common factors: 1, 2
Greatest common factor: 2
23. 84 and 105:
Common factors: 1, 3, 7, 21
Greatest common factor: 21
Find the greatest common factor of each pair of numbers.
25 and 140