prime factor of 273
Understand the Problem
The question is asking us to find the prime factors of the number 273. This involves breaking down the number into its prime components.
Answer
The prime factors of 273 are $3$, $7$, and $13$.
Answer for screen readers
The prime factors of 273 are $3$, $7$, and $13$.
Steps to Solve
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Start with the number Begin with the number 273 you want to factor.
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Check for divisibility by the smallest prime (2) Since 273 is an odd number, it is not divisible by 2. Proceed to the next smallest prime number.
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Check divisibility by the next prime (3) To check if 273 is divisible by 3, you can sum the digits: $2 + 7 + 3 = 12$. Since 12 is divisible by 3, so is 273. Divide 273 by 3: $$ 273 \div 3 = 91 $$
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Factor 91 Now, we need to factor 91. Check for divisibility by the next prime, which is 5. Since 91 does not end in 0 or 5, it is not divisible by 5. Check for the next prime, which is 7: $$ 91 \div 7 = 13 $$ This division shows that 91 can be factored into 7 and 13.
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Collect all the prime factors Now combine the prime factors from the divisions: $$ 273 = 3 \times 7 \times 13 $$
The prime factors of 273 are $3$, $7$, and $13$.
More Information
The number 273 can be expressed as the product of these three prime numbers. Each of these primes cannot be divided further, which confirms they are prime.
Tips
- Forgetting to check divisibility by all primes in order can lead to missing factors.
- Not summing the digits correctly when checking if a number is divisible by 3.
