78 as a product of prime factors
Understand the Problem
The question is asking us to express the number 78 as a product of its prime factors. This involves finding the prime numbers that multiply together to give 78.
Answer
The prime factorization of 78 is $78 = 2 \times 3 \times 13$.
Answer for screen readers
The prime factorization of 78 is
$$ 78 = 2 \times 3 \times 13 $$
Steps to Solve
- Identify the number to factor
We start with the number 78, and we need to find its prime factors.
- Divide by the smallest prime number
The smallest prime number is 2. Check if 78 is divisible by 2. Since 78 is even, we divide:
$$ 78 \div 2 = 39 $$
So, one of the prime factors is 2.
- Factor the remaining number
Now we need to factor 39. Start with the smallest prime number:
- Check if 39 is divisible by 2 (it is not).
- Next, check with 3:
$$ 39 \div 3 = 13 $$
So, another prime factor is 3.
- Identify if the last number is prime
Now we have the number 13. Since 13 is only divisible by 1 and itself, it is a prime number.
- Write the final result
Now, we can express 78 as a product of its prime factors. We have found the prime factorization:
$$ 78 = 2 \times 3 \times 13 $$
The prime factorization of 78 is
$$ 78 = 2 \times 3 \times 13 $$
More Information
Prime factorization is a way of expressing a number as the product of its prime numbers. It shows the fundamental building blocks of a number and is useful in various areas of mathematics, including number theory and simplification of fractions.
Tips
- Dividing only by prime numbers: Always start dividing by the smallest prime number and continue with the next smallest if the number isn't divisible.
- Forgetting to check if the last number is prime: Check that your final quotient after continuous division is indeed a prime.
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