What are the prime factors of 252?
Understand the Problem
The question is asking for the prime factors of the number 252, which involves identifying the prime numbers that multiply together to give 252. To solve this, we will factor 252 into its prime components.
Answer
The prime factors of 252 are $2^2 \times 3^2 \times 7$.
Answer for screen readers
The prime factors of 252 are $2^2 \times 3^2 \times 7$.
Steps to Solve
- Start with the number 252
We begin with the number 252. To factor this number, we need to divide it by the smallest prime numbers.
- Divide by the smallest prime (2)
Since 252 is an even number, we can divide it by 2.
$$ 252 \div 2 = 126 $$
- Continue dividing by 2
We can continue factoring 126 by dividing it by 2 again.
$$ 126 \div 2 = 63 $$
- Switch to the next smallest prime (3)
Now, we have 63, which is not divisible by 2. We try dividing by the next smallest prime number, 3.
$$ 63 \div 3 = 21 $$
- Continue with 3
Next, we divide 21 by 3:
$$ 21 \div 3 = 7 $$
- Identify that 7 is prime
Now we have reached 7, which is a prime number.
- Compile all prime factors
The prime factorization of 252 is:
$$ 2 \times 2 \times 3 \times 3 \times 7 $$
We can write this in exponential form as:
$$ 2^2 \times 3^2 \times 7 $$
The prime factors of 252 are $2^2 \times 3^2 \times 7$.
More Information
The prime factorization means breaking down a number into the prime numbers that multiply together to recreate the original number. Knowing prime factorization is vital in many areas of mathematics, including solving fractions and finding least common multiples.
Tips
- Confusing composite and prime numbers: Remember that prime numbers have only two factors (1 and themselves).
- Skipping re-evaluation of division by smaller primes: Always check for more divisions by smaller primes before moving on to larger ones.