find the greatest common factor (gcf).
21. 5, 7
22. 12, 15
23. 4, 6
24. 9, 11
25. 22, 44, 66
26. 77, 121
27. 80, 120
28. 20, 28
29. 2, 3, 4, 5, 7
30. 4, 6, 10, 22
31. 14, 21, 35, 70
32. 6, 10, 11, 14
33. 6, 15, 33, 48
34. 18, 45, 63, 81
35. 13, 39, 52, 78

Question

Accepted Answer

# Explanation:
## Step1: Prime - factorize the numbers
For each pair/group of numbers, we find their prime - factorizations.
## Step2: Identify common prime factors
We look for the prime factors that are common to all the numbers in the pair/group.
## Step3: Calculate the GCF
The GCF is the product of the common prime factors.

### 21. 5, 7
5 is prime ($5 = 5$) and 7 is prime ($7 = 7$). They have no common factors other than 1.
# Answer: 1

### 22. 12, 15
$12=2	imes2	imes3$, $15 = 3	imes5$. The common factor is 3.
# Answer: 3

### 23. 4, 6
$4 = 2	imes2$, $6=2	imes3$. The common factor is 2.
# Answer: 2

### 24. 9, 11
9 = 3×3, 11 is prime. They have no common factors other than 1.
# Answer: 1

### 25. 22, 44, 66
$22=2	imes11$, $44 = 2	imes2	imes11$, $66=2	imes3	imes11$. The common factors are $2	imes11 = 22$.
# Answer: 22

### 26. 77, 121
$77=7	imes11$, $121 = 11	imes11$. The common factor is 11.
# Answer: 11

### 27. 80, 120
$80=2	imes2	imes2	imes2	imes5$, $120=2	imes2	imes2	imes3	imes5$. The common factors are $2	imes2	imes2	imes5=40$.
# Answer: 40

### 28. 20, 28
$20=2	imes2	imes5$, $28=2	imes2	imes7$. The common factors are $2	imes2 = 4$.
# Answer: 4

### 29. 2, 3, 4, 5, 7
2 is prime, 3 is prime, 4 = 2×2, 5 is prime, 7 is prime. They have no common factors other than 1.
# Answer: 1

### 30. 4, 6, 10, 22
$4 = 2	imes2$, $6=2	imes3$, $10=2	imes5$, $22=2	imes11$. The common factor is 2.
# Answer: 2

### 31. 14, 21, 35, 70
$14=2	imes7$, $21=3	imes7$, $35=5	imes7$, $70=2	imes5	imes7$. The common factor is 7.
# Answer: 7

### 32. 6, 10, 11, 14
$6=2	imes3$, $10=2	imes5$, 11 is prime, $14=2	imes7$. The common factor is 2.
# Answer: 2

### 33. 6, 15, 33, 48
$6=2	imes3$, $15=3	imes5$, $33=3	imes11$, $48=2	imes2	imes2	imes2	imes3$. The common factor is 3.
# Answer: 3

### 34. 18, 45, 63, 81
$18=2	imes3	imes3$, $45=3	imes3	imes5$, $63=3	imes3	imes7$, $81=3	imes3	imes3	imes3$. The common factors are $3	imes3 = 9$.
# Answer: 9

### 35. 13, 39, 52, 78
$13$ is prime, $39=3	imes13$, $52=2	imes2	imes13$, $78=2	imes3	imes13$. The common factor is 13.
# Answer: 13

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QUESTION IMAGE

Question

Explanation:

Step1: Prime - factorize the numbers

Step2: Identify common prime factors

Step3: Calculate the GCF

21. 5, 7

Answer:

22. 12, 15