# What is the prime factorization of a 150? F) 2×2×25. G) 2×3×5×5 H) 5×30. J) 2×3×5

Jun 16, 2018

#### Explanation:

$2 \times 3 \times 5 \times 5$

$= 6 \times 5 \times 5$

$= 6 \times 25$

$= 150$

Therefore,

$150 = 2 \times 3 \times 5 \times 5$

Jun 16, 2018

$2 \times 3 \times 5 \times 5 \to G$

#### Explanation:

$\text{using the prime numbers } 2 , 3 , 5 , 7 , \ldots$

• " divide the number by 2"

• " if the quotient is 1 then finish"

• " if not repeat "

• " if 2 does not divide move onto 3"

• " repeat until a quotient of 1 is reached"

$150 \div \textcolor{red}{2} = 75 \leftarrow \textcolor{b l u e}{\text{move to 3}}$

$> 75 \div \textcolor{red}{3} = 25 \leftarrow \textcolor{b l u e}{\text{move to 5}}$

$25 \div \textcolor{red}{5} = 5 \leftarrow \textcolor{b l u e}{\text{repeat with 5}}$

$5 \div \textcolor{red}{5} = 1 \leftarrow \textcolor{b l u e}{\text{quotient of 1 reached}}$

$150 = \textcolor{red}{2} \times \textcolor{red}{3} \times \textcolor{red}{5} \times \textcolor{red}{5} \to G$