Jane writes down the prime
decomposition of 224 as .
Calculate the values of and .

Ask by Crawford Blake. in the United Kingdom

Jan 21,2025

Question

Jane writes down the prime decomposition of 224 as $$ 2^{a} 	imes b $$. Calculate the values of $$ a $$ and $$ b $$.

UpStudy AI · Accepted Answer

To find the values of $$ a $$ and $$ b $$ in the prime decomposition of 224 written as $$ 2^{a} \times b $$, we can follow these steps:

1. **Prime Factorization of 224**:
   
   Start by dividing 224 by the smallest prime number, which is 2, repeatedly until it is no longer divisible by 2.

$$
   \begin{align*}
   224 \div 2 &= 112 \
   112 \div 2 &= 56 \
   56 \div 2 &= 28 \
   28 \div 2 &= 14 \
   14 \div 2 &= 7 \
   \end{align*}
   $$

After dividing by 2 five times, we are left with 7, which is a prime number.

2. **Expressing in the Form $$ 2^{a} \times b $$**:
   
   From the above, we have:
   
   $$
   224 = 2^5 \times 7
   $$
   
   Here, $$ a = 5 $$ and $$ b = 7 $$.

**Final Answer:**
$$
a = 5 \quad \text{and} \quad b = 7
$$
$$ a = 5 $$ and $$ b = 7 $$.

Jane writes down the prime
decomposition of 224 as .
Calculate the values of and .

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Jane writes down the prime decomposition of 224 as . Calculate the values of and .