Write the prime factorization of 70.
Understand the Problem
The question is asking for the prime factorization of the number 70, which involves breaking it down into its prime components.
Answer
The prime factorization of 70 is $2 \times 5 \times 7$.
Answer for screen readers
The prime factorization of 70 is $2 \times 5 \times 7$.
Steps to Solve
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Identify the smallest prime number
Start with the smallest prime number, which is 2. Check if 2 divides 70 evenly. Since $70 \div 2 = 35$, we have found one prime factor. -
Use the quotient to continue factoring
Next, take the quotient 35 and check for divisibility by the next smallest prime number, which is 3. Since $35 \div 3$ is not a whole number, move to the next prime, which is 5. -
Divide by the next prime number
Now check 35 for divisibility by 5. Since $35 \div 5 = 7$, we found another prime factor. -
Identify the last prime factor
Now, check the quotient 7. The number 7 is also a prime number, and it cannot be factored further. -
Compile the prime factors
The prime factorization of 70 is then the product of the prime numbers we found: $$ 70 = 2 \times 5 \times 7 $$
The prime factorization of 70 is $2 \times 5 \times 7$.
More Information
Prime factorization is a way of expressing a number as a product of its prime numbers. It is useful in various areas of mathematics, such as simplifying fractions, finding least common multiples, and solving problems related to divisibility.
Tips
One common mistake is attempting to divide by non-prime numbers or larger primes without checking if the number is divisible. Always start with the smallest prime and work your way up.
