Question

number theory
gcf practice b
find the greatest common factor.
24 and 36
36 and 54
65 and 44
58 and 65
96 and 24
and 102
and 38
and 19
59 and 57
72 and 60
80 and 64
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Explanation:

Step1: Factor 44 and 40

Factors of 44: $1,2,4,11,22,44$; Factors of 40: $1,2,4,5,8,10,20,40$

Step2: Find GCF of 44 and 40

Common factors: $1,2,4$; GCF = $4$
---

Step1: Factor 36 and 16

Factors of 36: $1,2,3,4,6,9,12,18,36$; Factors of 16: $1,2,4,8,16$

Step2: Find GCF of 36 and 16

Common factors: $1,2,4$; GCF = $4$
---

Step1: Factor 64 and 40

Factors of 64: $1,2,4,8,16,32,64$; Factors of 40: $1,2,4,5,8,10,20,40$

Step2: Find GCF of 64 and 40

Common factors: $1,2,4,8$; GCF = $8$
---

Step1: Factor 18 and 24

Factors of 18: $1,2,3,6,9,18$; Factors of 24: $1,2,3,4,6,8,12,24$

Step2: Find GCF of 18 and 24

Common factors: $1,2,3,6$; GCF = $6$
---

Step1: Factor 36 and 44

Factors of 36: $1,2,3,4,6,9,12,18,36$; Factors of 44: $1,2,4,11,22,44$

Step2: Find GCF of 36 and 44

Common factors: $1,2,4$; GCF = $4$
---

Step1: Factor 39 and 57

Factors of 39: $1,3,13,39$; Factors of 57: $1,3,19,57$

Step2: Find GCF of 39 and 57

Common factors: $1,3$; GCF = $3$
---

Step1: Factor 55 and 65

Factors of 55: $1,5,11,55$; Factors of 65: $1,5,13,65$

Step2: Find GCF of 55 and 65

Common factors: $1,5$; GCF = $5$
---

Step1: Factor 72 and 60

Factors of 72: $1,2,3,4,6,8,9,12,18,24,36,72$; Factors of 60: $1,2,3,4,5,6,10,12,15,20,30,60$

Step2: Find GCF of 72 and 60

Common factors: $1,2,3,4,6,12$; GCF = $12$
---

Step1: Factor 96 and 24

Factors of 96: $1,2,3,4,6,8,12,16,24,32,48,96$; Factors of 24: $1,2,3,4,6,8,12,24$

Step2: Find GCF of 96 and 24

Common factors: $1,2,3,4,6,8,12,24$; GCF = $24$
---

Step1: Factor 80 and 64

Factors of 80: $1,2,4,5,8,10,16,20,40,80$; Factors of 64: $1,2,4,8,16,32,64$

Step2: Find GCF of 80 and 64

Common factors: $1,2,4,8,16$; GCF = $16$

Answer:

1. 44 and 40: $\boldsymbol{4}$
2. 36 and 16: $\boldsymbol{4}$
3. 64 and 40: $\boldsymbol{8}$
4. 18 and 24: $\boldsymbol{6}$
5. 36 and 44: $\boldsymbol{4}$
6. 39 and 57: $\boldsymbol{3}$
7. 55 and 65: $\boldsymbol{5}$
8. 72 and 60: $\boldsymbol{12}$
9. 96 and 24: $\boldsymbol{24}$
10. 80 and 64: $\boldsymbol{16}$