What is the prime factorization of 1287?
Understand the Problem
The question is asking for the prime factorization of the number 1287, which involves finding the prime numbers that multiply together to give the original number.
Answer
The prime factorization of 1287 is $3^2 \cdot 11 \cdot 13$.
Answer for screen readers
The prime factorization of 1287 is $3^2 \cdot 11 \cdot 13$.
Steps to Solve
-
Initial Division by Smallest Prime Begin by testing the smallest prime number, which is 2. Since 1287 is an odd number, it is not divisible by 2.
-
Dividing by the Next Prime: 3 Next, check divisibility by 3. You can add the digits of 1287: $$ 1 + 2 + 8 + 7 = 18 $$ Since 18 is divisible by 3, so is 1287. Now divide: $$ 1287 \div 3 = 429 $$
-
Continue Dividing by 3 Now, take 429 and divide it by 3 again: $$ 429 \div 3 = 143 $$
-
Dividing 143 by the Next Prime: 11 Next, check if 143 can be divided by small primes like 5 or 7. It’s not divisible by these; then try 11: $$ 143 \div 11 = 13 $$ Now we have reached a prime number.
-
Combining the Factors We can now write the prime factorization of 1287 by combining the factors we found: $$ 1287 = 3^2 \cdot 11 \cdot 13 $$
The prime factorization of 1287 is $3^2 \cdot 11 \cdot 13$.
More Information
Finding the prime factorization is useful in various areas of mathematics, such as simplifying fractions, finding the greatest common divisor (GCD), or even in number theory. The process can also help in understanding the structure of numbers.
Tips
- A common mistake is not checking divisibility by all relevant small primes. Always test divisibility with 2, 3, 5, 7, 11, etc., particularly for composite numbers.
- Miscalculating the division or missing a factor can lead to incorrect results. Always double-check your division calculations.
