Question

what is the prime factorization of 70?
2 × 35 2 × 2 × 5 × 7
2 × 5 × 14 2 × 5 × 7
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lesson: prime factorization

Explanation:

Step1: Recall prime factorization

Prime factorization means expressing a number as a product of prime numbers. A prime number is a number greater than 1 that has no positive divisors other than 1 and itself.

Step2: Factorize 70

Start by dividing 70 by the smallest prime number, 2. So, \(70\div2 = 35\). Now, factorize 35. The next smallest prime number that divides 35 is 5. So, \(35\div5=7\). And 7 is a prime number. So, combining these, we get \(70 = 2\times5\times7\).

Step3: Analyze the options

• Option 1: \(2\times35\) - 35 is not a prime number (since \(35 = 5\times7\)), so this is not a prime factorization.
• Option 2: \(2\times2\times5\times7=140

eq70\), so this is incorrect.

• Option 3: \(2\times5\times14\) - 14 is not a prime number (since \(14 = 2\times7\)), so this is not a prime factorization.
• Option 4: \(2\times5\times7\) - All 2, 5, and 7 are prime numbers, and their product is 70.

Answer:

The correct option is the one with \(2\times5\times7\) (the fourth option in the given choices).