Prime factor of 275
Understand the Problem
The question is asking for the prime factors of the number 275. To find the prime factors, we will need to break down the number into its smallest divisible prime numbers.
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
- Identify divisibility by the smallest prime number
Start with the smallest prime number, which is 2. Since 275 is odd, it is not divisible by 2.
- Test for divisibility by the next prime number
Now, test the next smallest prime, which is 3. Calculate the sum of the digits of 275: $$ 2 + 7 + 5 = 14 $$ Since 14 is not divisible by 3, 275 is also not divisible by 3.
- Continue testing with the next prime
Next, check divisibility by 5, as 275 ends in 5. We can divide: $$ 275 \div 5 = 55 $$ So, 5 is a prime factor.
- Factor the quotient further
Now, take the quotient 55 and factor it. We can check for divisibility by 5 again: $$ 55 \div 5 = 11 $$ Thus, 5 is another prime factor.
- Identify the last prime factor
The quotient we are left with is 11, which is also a prime number.
- Compile the prime factors
From our calculations, we find that the prime factors of 275 are: $$ 5, 5, 11 $$ which is typically written as: $$ 5^2 \times 11 $$
The prime factorization of 275 is $5^2 \times 11$.
More Information
275 can be expressed as a product of primes. This not only helps in understanding its structure but also has applications in number theory and cryptography.
Tips
- Forgetting to check all small primes: Sometimes, people skip smaller primes or jump to larger primes too quickly.
- Misunderstanding division with prime factors: It's crucial to not mix factors or assume a composite number without confirming it through division.
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