Question

in 6–8, write the prime factorization of each number. if the number is prime, write prime. 8 13 1/2, 4, 8, 10, 32 19 prime in 9–11, find the gcf for each pair of numbers. 9 18, 36 18 - 18 36 - 18 10 22, 55 22 - 11 55 - 11 11 1001, 48 1001 - 1 48 - 1 in 12–14, find the lcm for each pair of numbers. 12 2, 5 2 - 10 5 - 10 8, 12 8 - 24 12 - 24 8, 10 8 - 40 10 - 40

Explanation:

Let's solve these problems step by step. We'll start with the GCF problems (9 - 11) and then the LCM problems (12 - 14).

Problem 9: Find GCF of 18 and 36

Step 1: Prime Factorization of 18

Prime factors of 18: \(18 = 2\times3\times3\)

Step 2: Prime Factorization of 36

Prime factors of 36: \(36 = 2\times2\times3\times3\)

Step 3: Identify Common Factors

The common prime factors are \(2\), \(3\), and \(3\).

Step 4: Calculate GCF

Multiply the common prime factors: \(2\times3\times3 = 18\)

Step 1: Prime Factorization of 22

Prime factors of 22: \(22 = 2\times11\)

Step 2: Prime Factorization of 55

Prime factors of 55: \(55 = 5\times11\)

Step 3: Identify Common Factors

The common prime factor is \(11\).

Step 4: Calculate GCF

The GCF is \(11\) (since it's the only common prime factor).

Step 1: Prime Factorization of 1001

Prime factors of 1001: \(1001 = 7\times11\times13\) (you can check by dividing 1001 by 7, 11, 13)

Step 2: Prime Factorization of 48

Prime factors of 48: \(48 = 2\times2\times2\times2\times3\)

Step 3: Identify Common Factors

There are no common prime factors between 1001 and 48 (other than 1, since 1 is a factor of every number).

Step 4: Calculate GCF

The GCF is \(1\) (since the only common factor is 1).

Answer:

18

Problem 10: Find GCF of 22 and 55