prime factorisation of 630
Understand the Problem
The question is asking for the prime factorization of the number 630, which means we need to express 630 as a product of its prime factors.
Answer
The prime factorization of 630 is \( 2 \times 3^2 \times 5 \times 7 \).
Answer for screen readers
The prime factorization of 630 is ( 2 \times 3^2 \times 5 \times 7 ).
Steps to Solve

Start with the original number We begin with the number 630.

Divide by the smallest prime number Start dividing 630 by the smallest prime number, which is 2. $$ 630 \div 2 = 315 $$

Continue with the next smallest prime Next, we take 315 and divide it by the next smallest prime number, which is 3. $$ 315 \div 3 = 105 $$

Repeat the process Now, we take 105 and divide it by 3 again (the next smallest prime). $$ 105 \div 3 = 35 $$

Next prime number Now we take 35 and divide it by the next smallest prime number, which is 5. $$ 35 \div 5 = 7 $$

Last step Finally, we are left with 7, which is also a prime number, so we stop here.

Combine the prime factors Now, we can write 630 as a product of its prime factors: $$ 630 = 2 \times 3^2 \times 5 \times 7 $$
The prime factorization of 630 is ( 2 \times 3^2 \times 5 \times 7 ).
More Information
The prime factorization shows that 630 is made up of the primes 2, 3, 5, and 7. This decomposition can be helpful in understanding the number's properties, such as its divisibility and in simplifying fractions.
Tips
 Forgetting to confirm that factors are prime can lead to providing incorrect factorizations. Always check that all factors are indeed prime.
 Not listing the prime factors in exponential form (e.g., writing ( 3^2 ) instead of ( 3 \times 3 )) can lead to confusion.