prime factor of 630
Understand the Problem
The question is asking for the prime factors of the number 630. To solve this, we will determine which prime numbers multiply together to yield 630.
Answer
The prime factors of 630 are $2$, $3^2$, $5$, and $7$.
Answer for screen readers
The prime factors of 630 are $2$, $3^2$, $5$, and $7$.
Steps to Solve
- Start with the number 630
To find the prime factors of 630, start by dividing the number by the smallest prime, which is 2.
- Divide by 2
Since 630 is even, we can divide it by 2:
$$ 630 \div 2 = 315 $$
- Next prime: 3
Now, we need to see if 315 is divisible by the next prime number, which is 3. The sum of the digits of 315 is 3 + 1 + 5 = 9, which is divisible by 3.
Now divide:
$$ 315 \div 3 = 105 $$
- Continue with 3
Now check 105:
$$ 105 \div 3 = 35 $$
- Next prime: 5
Now check if 35 is divisible by the next prime number, which is 5. Since the last digit is 5, we can divide:
$$ 35 \div 5 = 7 $$
- Final prime: 7
The last number we have is 7, which is a prime number itself.
- List all prime factors
Now, compile all the prime factors found in the steps above:
The prime factors of 630 are: $2$, $3$, $3$, $5$, and $7$. We can express it as:
$$ 630 = 2 \times 3^2 \times 5 \times 7 $$
The prime factors of 630 are $2$, $3^2$, $5$, and $7$.
More Information
Prime factorization is a fundamental concept in number theory, which shows how numbers can be expressed as products of prime numbers. The process of determining prime factors can help in various applications, such as simplifying fractions and finding least common multiples.
Tips
- Forgetting to check all prime numbers: Make sure to test divisibility by all prime numbers sequentially until you reach a square root of the number being factored.
- Miscounting multiplicities of prime factors: Be careful to track how many times each prime divides the number.
