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The ideas in this lesson are taken from Multiplication Division 3 ebook. Only a few examples of each problem type are shown; you should make more problems of each kind for the student. Factoring, part 3
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To find all the prime numbers less than 100 we can use the sieve of Eratosthenes.
The explanation why you don't have to check The numbers that are not crossed out are primes. List here all primes between 0 and 30: ____________________________________________________________ |
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We have found how to know if a number is divisible by 2, 5, 10, 3, or 9. We can use that in factoring.
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Example problems
1. Factor the following numbers so the factors are prime numbers. Do any needed long divisions in your notebook.
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90
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165 / \
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95 / \
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We can use divisibility rules in factoring bigger numbers, too. Look at the
examples.
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2. Circle or underline the number that the following numbers are divisible by. Use divisibility rules. Then pick the GREATEST divisor of those, do the division, and express the number as a product. Do the long divisions in your notebook. Follow the example given.
| Number |
Divisible by |
Division |
Expression
as a product |
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260 |
10 5 3 2 |
260 10 = 26 | 260 = 10 × 26 |
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96 |
10 5 3 2 |
96 __ = ___ | 96 = ___ × __ |
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95 |
10 5 3 2 |
95 __ = ___ | 95 = ___ × __ |
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132 |
10 5 3 2 |
132 __ = ___ | 132 = ___ × __ |
3. Use the previous exercise and factor these numbers. Continue factoring to prime factors.
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4. Factor the following numbers in your notebook down to prime factors. You can start factoring by any number that you notice it is divisible by! Try first if the number is divisible by 10, then by 5, then by 2, then by 3 or 9.
306 =990 =
945 =
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Many times primes occur in pairs so that their difference is only two. For example, 5 and 7 are such a pair, so are 11 and 13. Find all such pairs that are less than 100. Use the sieve of Eratosthenes. |
The fast, FUN, and easy way to learn multiplication. Learn the upper times tales in two sittings using mnemonic stories.
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