What is the prime factorization of 735?
Understand the Problem
The question is asking for the prime factorization of the number 735, which involves finding the prime numbers that multiply together to give the number 735.
Answer
The prime factorization of 735 is $3 \times 5 \times 7^2$.
Answer for screen readers
The prime factorization of 735 is $3 \times 5 \times 7^2$.
Steps to Solve
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Start with the number First, we start with the number 735.
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Check for divisibility by 2 The number 735 is odd, so it is not divisible by 2.
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Check for divisibility by 3 Next, we check if 735 is divisible by 3 by adding the digits: $7 + 3 + 5 = 15$. Since 15 is divisible by 3, we divide: $$ 735 \div 3 = 245 $$
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Check for divisibility of the result by 5 Now we check if 245 is divisible by 5. Since it ends in 5, it is divisible: $$ 245 \div 5 = 49 $$
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Factor 49 Next, we factor 49. Since $49 = 7 \times 7$, we can write it as: $$ 49 = 7^2 $$
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Combine the factors Now we can combine all the factors obtained: $$ 735 = 3 \times 5 \times 7^2 $$
The prime factorization of 735 is $3 \times 5 \times 7^2$.
More Information
The prime factorization represents the prime numbers that multiply together to reach the given number. Prime factorization is useful in many areas of mathematics, such as finding the least common multiple or greatest common divisor of numbers.
Tips
- Forgetting to check divisibility for all prime numbers sequentially. Make sure to check primes such as 3, 5, 7, etc., in order.
- Confusing prime factors with non-prime numbers. Ensure you only use prime numbers in the final factorization.
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