Find the prime factors of 63.
Understand the Problem
The question is asking for the prime factors of the number 63. Prime factors are the prime numbers that multiply together to give the original number. To solve this, we will find the prime numbers that can divide 63 evenly.
Answer
The prime factors of 63 are $3$ and $7$.
Answer for screen readers
The prime factors of 63 are $3$ and $7$ (with $3$ being squared).
Steps to Solve
- Start with the number 63
Begin with the number for which we need to find the prime factors, which is 63.
- Find the smallest prime number that divides 63
The smallest prime number is 2. Since 63 is odd, it is not divisible by 2.
- Test the next prime numbers
Next, check 3. Since $63 \div 3 = 21$, 3 is a prime factor.
- Divide 63 by 3 and find the next factor
Now, take the quotient and continue factoring:
$$21 \div 3 = 7$$
So now we have found another prime factor, which is also 3.
- Check if 7 is a prime number
The quotient now is 7, which is a prime number itself and cannot be divided further by any prime factors except for 1 and 7.
- Compile the prime factors
Now we compile the prime factors. The prime factorization of 63 is $3^2 \times 7$.
The prime factors of 63 are $3$ and $7$ (with $3$ being squared).
More Information
63 can be expressed as the product of its prime factors as follows: $63 = 3^2 \times 7$.
Tips
- Forgetting to check for factors beyond the smallest primes.
- Miscalculating the division when finding subsequent factors.
