224 as a product of powers of its prime factors

To express 224 as a product of powers of its prime factors, follow these steps:

1. Start by dividing 224 by the smallest prime, 2:
   \[
   224 \div 2 = 112
   \]
2. Divide 112 by 2 again:
   \[
   112 \div 2 = 56
   \]
3. Continue dividing by 2:
   \[
   56 \div 2 = 28
   \]
4. Divide 28 by 2:
   \[
   28 \div 2 = 14
   \]
5. Divide 14 by 2:
   \[
   14 \div 2 = 7
   \]
6. Now, 7 is a prime number, so stop here.

Thus, the prime factorization of 224 is:
\[
224 = 2^5 \times 7
\]

Would you like further explanation or have any other questions?

Here are 5 related questions to deepen your understanding:
1. How would you find the prime factorization of a larger number?
2. What is the greatest common divisor (GCD) of 224 and 56?
3. How can you use prime factorization to simplify fractions?
4. Can you express 1000 as a product of its prime factors?
5. What is the least common multiple (LCM) of 224 and 14?

**Tip:** Always start with the smallest prime number (2) when factoring even numbers.

Learn how to express 224 as a product of powers of its prime factors. Follow a detailed breakdown that involves dividing by the smallest primes, using exponents, and applying the fundamental theorem of arithmetic. Perfect for students in Grades 5-7.

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