What are the prime factors of 1260?
Understand the Problem
The question is asking for the prime factorization of the number 1260, which involves breaking it down into its prime factors.
Answer
The prime factorization of 1260 is $2^2 \times 3^2 \times 5^1 \times 7^1$.
Answer for screen readers
The prime factorization of 1260 is $2^2 \times 3^2 \times 5^1 \times 7^1$.
Steps to Solve
- Start with the Number
Begin with the number 1260. We will divide this number by the smallest prime number.
- Divide by the Smallest Prime
Divide 1260 by 2, which is the smallest prime number: $$ 1260 \div 2 = 630 $$ So, we have the first prime factor: 2.
- Continue Dividing by 2
Now, divide 630 by 2 again: $$ 630 \div 2 = 315 $$ This gives us another factor of 2.
- Switch to the Next Smallest Prime
315 is not divisible by 2, so we try the next prime number, which is 3: $$ 315 \div 3 = 105 $$ We found another prime factor: 3.
- Continue Dividing by 3
Next, divide 105 by 3 again: $$ 105 \div 3 = 35 $$ This gives us another factor of 3.
- Switch to the Next Prime
Now, 35 is not divisible by 3, so we check 5: $$ 35 \div 5 = 7 $$ This gives us a factor of 5.
- Recognize a Prime Factor
Finally, we are left with 7, which is a prime number.
- Write the Prime Factorization
Now we can write the complete prime factorization: $$ 1260 = 2^2 \times 3^2 \times 5^1 \times 7^1 $$
The prime factorization of 1260 is $2^2 \times 3^2 \times 5^1 \times 7^1$.
More Information
The prime factorization represents how a number can be expressed as a product of prime numbers. Prime numbers are those greater than 1, which have no divisors other than 1 and themselves. Understanding prime factorization is important in number theory and plays a role in various applications such as simplification of fractions and finding least common multiples.
Tips
- Forgetting to account for all prime factors can lead to incomplete factorizations. Always ensure each prime factor's contribution is included and noted with the correct exponent.
- Sometimes students might apply divisibility incorrectly; practicing the division with different prime numbers helps build accuracy.
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