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A football team’s record is 75 wins and 25 losses.
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Express these numbers as products of their prime factors.
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Writing a number as the product of its prime factors is also known as prime factorization.
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We know that any prime number has exactly two factors, one and itself.
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The only even prime number is two.
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The next five prime numbers after this are three, five, seven, 11, and 13.
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All of these numbers are only divisible by one and the number itself.
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In order to write the numbers 75 and 25 as products of their prime factors, we can use a factor tree.
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Let’s begin with 25.
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The only prime number that divides exactly into 25 is five.
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This is because it is a square number; five multiplied by five or five squared is 25.
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Our factor tree is completed.
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And 25 is equal to five squared.
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The smallest prime number that divides into 75 is three.
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As three multiplied by 25 is 75, these are our two branches.
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Three is prime, so we can circle this.
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And this path is finished.
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As we have already seen, 25 is equal to five multiplied by five.
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As both of these are prime, our factor tree once again is complete.
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75 written as a product of its prime factors is three multiplied by five squared.
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Whenever possible, we wrote these answers in exponent form.
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The answer for 75 could also be written as five squared multiplied by three.
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And the multiplication sign could be replaced by a dot.