What is the prime factorization of 275?
Understand the Problem
The question is asking for the prime factorization of the number 275, which involves breaking it down into its prime number factors. The prime factorization process typically starts by dividing the number by the smallest prime numbers until all the factors are prime.
Answer
The prime factorization of 275 is $5^2 \times 11$.
Answer for screen readers
The prime factorization of 275 is $5^2 \times 11$.
Steps to Solve
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Start with the smallest prime number
Begin by dividing 275 by the smallest prime number, which is 2. Since 275 is odd, it is not divisible by 2. -
Check the next prime number, 3
Next, check if 275 is divisible by 3 by adding the digits together: $2 + 7 + 5 = 14$. Since 14 is not divisible by 3, 275 is not divisible by 3. -
Check the next prime number, 5
Since 275 ends in a 5, it is divisible by 5. We perform the division:
$$ 275 \div 5 = 55 $$
So, we have $275 = 5 \times 55$. -
Factor 55
Next, we factor 55. Again, we start with the smallest primes. 55 is odd and not divisible by 2 or 3, but it is divisible by 5:
$$ 55 \div 5 = 11 $$
Now, we have $55 = 5 \times 11$. -
Combine factors
Putting it all together, we have:
$$ 275 = 5 \times 5 \times 11 $$
or, more succinctly, as powers of primes:
$$ 275 = 5^2 \times 11 $$
The prime factorization of 275 is $5^2 \times 11$.
More Information
The number 275 is interesting because it is the product of a square of a prime number (5) and another prime number (11). This type of factorization is useful in various mathematical applications, including finding the least common multiple and greatest common divisor.
Tips
- Not checking divisibility by small prime numbers systematically. Ensure that you test each smaller prime before moving to larger ones.
- Forgetting to fully factor a composite number and leaving large non-prime factors.
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