What are the prime factors of 275?

Understand the Problem

The question is asking for the prime factors of the number 275, which involves identifying the prime numbers that multiply together to give 275.

Answer

The prime factors are $5$ and $11$.

Steps to Solve

Start with the number
We want to find the prime factors of 275.
Divide by the smallest prime
Begin by dividing 275 by the smallest prime number, which is 2.
Since 275 is odd, it is not divisible by 2.
Try the next prime, which is 3
Divide 275 by 3.
The result of the division is not an integer, so 275 is not divisible by 3.
Next prime number is 5
Now divide 275 by 5.
$$ 275 \div 5 = 55 $$
So, 5 is one of the prime factors.
Factor the quotient
Now, we need to factor 55 further.
Divide 55 by the smallest prime, again starting with 2.
55 is odd, so it's not divisible by 2.
Try dividing by 3
55 is not divisible by 3.
Check next prime, which is 5
Divide 55 by 5.
$$ 55 \div 5 = 11 $$
So, 5 is again a factor.
Factor the last quotient
Now we have the number 11, which is a prime number. Thus, we stop here.
Combine the prime factors
Putting it all together, the prime factorization of 275 is: $$ 275 = 5^2 \times 11 $$

The prime factors of 275 are $5$ and $11$.

More Information

The number 275 can also be expressed as $5 \times 5 \times 11$. Prime factorization helps in various areas of mathematics, including simplifying fractions and finding the least common multiple.

Tips

Confusing composite numbers for prime numbers: Remember, prime numbers only have two distinct positive divisors: 1 and itself.
Forgetting to test all prime numbers up to the square root of the number being factored.

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