Question

1. find the gcf:

a. 16 and 54
b. 25 and 30

1. find the lcm:

a. 5 and 8
b. 3 and 10

1. the ratio of men to women on a airplane is 3:4, which means…
2. a car travels 180 miles in 3 hours, which is a rate of ______ per hour.

Explanation:

Problem 1: Find the GCF

Part a: 16 and 54

Step1: Prime factorize 16

$16 = 2 \times 2 \times 2 \times 2$

Step2: Prime factorize 54

$54 = 2 \times 3 \times 3 \times 3$

Step3: Identify common prime factors

The common prime factor is 2 (with the lowest power of 1).

Step1: Prime factorize 25

$25 = 5 \times 5$

Step2: Prime factorize 30

$30 = 2 \times 3 \times 5$

Step3: Identify common prime factors

The common prime factor is 5 (with the lowest power of 1).

Step1: Prime factorize 5

$5 = 5$

Step2: Prime factorize 8

$8 = 2 \times 2 \times 2$

Step3: Multiply all prime factors (highest powers)

$LCM = 2^3 \times 5 = 8 \times 5 = 40$

Answer:

2

Part b: 25 and 30