Math Problem Statement

Express 882 as a product of its prime factors. Give your answer in index form.

Solution

To express 882 as a product of its prime factors and provide the answer in index form, we will first perform prime factorization.

Step 1: Start by dividing 882 by the smallest prime number (2).

  • 882÷2=441882 \div 2 = 441

Step 2: Now factorize 441 by the next smallest prime (since 441 is odd, divide by 3).

  • 441÷3=147441 \div 3 = 147

Step 3: Factorize 147 by 3 again.

  • 147÷3=49147 \div 3 = 49

Step 4: Factorize 49 by 7 (since 49 is 727^2).

  • 49÷7=749 \div 7 = 7
  • 7÷7=17 \div 7 = 1

Prime Factorization of 882:

  • 882=2×32×72882 = 2 \times 3^2 \times 7^2

Thus, the prime factorization of 882 in index form is: 882=2×32×72882 = 2 \times 3^2 \times 7^2

Would you like further details on prime factorization or any related topics?

Here are 5 questions to expand your understanding:

  1. How can you verify the prime factorization of any number?
  2. What are the steps to perform prime factorization on a large number?
  3. Why are prime factorizations important in number theory?
  4. What is the difference between index form and standard form of a number?
  5. How can prime factorization be used to find the greatest common divisor (GCD) of two numbers?

Tip: Always start with the smallest prime (2) when doing prime factorization.

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Math Problem Analysis

Mathematical Concepts

Prime Factorization
Exponents

Formulas

Prime Factorization: dividing by smallest primes
Index form: using exponents for repeated prime factors

Theorems

Fundamental Theorem of Arithmetic

Suitable Grade Level

Grades 7-9