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Write 75 as a product of its prime factors. - OCR - GCSE Maths - Question 1 - 2020 - Paper 1

Question 1

Write 75 as a product of its prime factors.

Worked Solution & Example Answer:Write 75 as a product of its prime factors. - OCR - GCSE Maths - Question 1 - 2020 - Paper 1

Step 1

Step 1: Identify the Prime Factors of 75

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Answer

To express 75 as a product of its prime factors, we begin by dividing 75 by the smallest prime number, which is 2. Since 75 is odd, we move to the next prime number, 3.

Dividing 75 by 3 gives:

$75 \, \div \, 3 = 25$

Next, we need to factor 25.

Step 2

Step 2: Factor 25

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Answer

The number 25 can also be factored. We note that:

$25 \, \div \, 5 = 5$

Thus, 25 can be expressed as:

$25 = 5 \times 5$

Step 3

Step 3: Combine All Prime Factors

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Answer

Putting it all together, we can express 75 as:

$75 = 3 \times 5 \times 5$

In exponential form, the product of its prime factors is:

$75 = 3 \times 5^2$

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