Pollard Haynes
07/29/2023 · Elementary School
\begin{tabular}{l} Exercise 2.5 \\ \( \begin{array}{lll}\text { 1. Express each of the following numbers as prime factorization form. } \\ \begin{array}{lll}\text { a. } 21 & \text { b. } 70 & \text { c. } 105\end{array} \\ \begin{array}{lll}\text { d. } 252 & \text { e. } 360 & \text { f. } 1,848\end{array} \\ \text { 2. } 180 \text { can be written as } 2^{a} \times 3^{b} \times 5^{c} \text {. Then, find the value of } a, b \text { and } c \text {. } \\ \text { 3. Find the four prime numbers whose product is } 462 .\end{array} \) \\ \hline\end{tabular}
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1. Prime factorizations:
- a. \( 21 = 3^1 \times 7^1 \)
- b. \( 70 = 2^1 \times 5^1 \times 7^1 \)
- c. \( 105 = 3^1 \times 5^1 \times 7^1 \)
- d. \( 252 = 2^2 \times 3^2 \times 7^1 \)
- e. \( 360 = 2^3 \times 3^2 \times 5^1 \)
- f. \( 1,848 = 2^3 \times 3^1 \times 7^1 \times 11^1 \)
2. Values of \( a, b, c \) for 180:
- \( a = 2, b = 2, c = 1 \)
3. Four prime numbers whose product is 462:
- 2, 3, 7, 11
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