Write 70 as a product of prime factors.
Understand the Problem
The question is asking for the prime factorization of the number 70, which involves breaking it down into the prime numbers that multiply together to yield 70.
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 by dividing the number 70 by the smallest prime number, which is 2. Since 70 is even, we can divide it by 2. $$ 70 \div 2 = 35 $$
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Continue with the next smallest prime Next, we check if 35 can be divided by the next smallest prime number, which is 3. Since 35 is not divisible by 3, we move to the next prime number, which is 5. $$ 35 \div 5 = 7 $$
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Recognize that 7 is prime Now, 7 is the last number we have. It is a prime number itself, and cannot be divided further by any prime number except for itself.
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Combine the factors Now we can express 70 as the product of the prime factors we found: $$ 70 = 2 \times 5 \times 7 $$
The prime factorization of 70 is $2 \times 5 \times 7$.
More Information
The number 70 is a composite number and can be expressed in terms of its prime factors. Understanding prime factorization is useful in various areas of mathematics, including simplifying fractions and solving problems related to divisibility.
Tips
- Forgetting that 1 is not a prime number. When starting prime factorization, some may mistakenly include 1.
- Not checking for divisibility by all prime numbers before moving to the next. Always ensure to test all smaller prime numbers.
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