Question

1. 30, 25, 10
2. 10, 4, 18

Explanation:

Problem 21: Find the greatest common divisor (GCD) of 30, 25, 10

Step1: Factorize each number

$30 = 2 \times 3 \times 5$
$25 = 5 \times 5$
$10 = 2 \times 5$

Step2: Identify common factors

The common prime factor among 30, 25, and 10 is 5.

Step3: Determine GCD

The greatest common divisor is the product of the common prime factors with the lowest exponent. Here, the common factor is 5 (exponent 1 in all factorizations). So, GCD is 5.

Problem 23: Find the greatest common divisor (GCD) of 10, 4, 18

Step1: Factorize each number

$10 = 2 \times 5$
$4 = 2 \times 2$
$18 = 2 \times 3 \times 3$

Step2: Identify common factors

The common prime factor among 10, 4, and 18 is 2.

Step3: Determine GCD

The greatest common divisor is the product of the common prime factors with the lowest exponent. Here, the common factor is 2 (exponent 1 in all factorizations). So, GCD is 2.

Answer:

s:
Problem 21: $\boldsymbol{5}$
Problem 23: $\boldsymbol{2}$