write 78 as a product of prime factors
Understand the Problem
The question is asking for the prime factorization of the number 78, which means we need to express 78 as the product of its prime factors. We will determine which prime numbers multiply together to give us 78.
Answer
The prime factorization of 78 is $2 \times 3 \times 13$.
Answer for screen readers
The prime factorization of 78 is $2 \times 3 \times 13$.
Steps to Solve
- Identify the smallest prime factor Start by dividing 78 by the smallest prime number, which is 2. Since 78 is even, it is divisible by 2.
$$ 78 \div 2 = 39 $$
- Find the next prime factor Next, check the result, 39, for its smallest prime factor. The smallest prime number that divides 39 is 3.
$$ 39 \div 3 = 13 $$
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Check if the result is prime Now check if 13 is a prime number. A prime number has no other factors other than 1 and itself. Since 13 cannot be divided evenly by any number other than 1 and 13, it is prime.
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Write the prime factorization Now, we can write the prime factorization of 78 using the factors we've found: $$ 78 = 2 \times 3 \times 13 $$
The prime factorization of 78 is $2 \times 3 \times 13$.
More Information
Prime factorization helps in understanding the structure of numbers and is fundamental in number theory. Knowing prime factors is useful in many areas of mathematics, including simplifying fractions and solving algebraic equations.
Tips
- Forgetting that a number must be divided by prime numbers only.
- Assuming that all composite numbers can only be divided by the smallest prime number without checking for other factors first.
