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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 and prime numbers
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In any multiplication the numbers that are multiplied are called factors
and the result is called a product.
From this multiplication fact we can make two division facts: |
1. Express each number as a product of two factors. Sometimes there are several ways of doing this and you can choose which way you like, but don't use 1 × the number itself. Look at the example. This process is called factoring.
| product | factors | product | factors | product | factors | ||
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10 = 50 = 24 = |
5 × 2 |
12 = 22 = 110 = |
94 = 121 = 40 = |
2. Express each number as a product of two factors and then make division facts and state by which numbers it is divisible. Look at the examples. Sometimes there are many ways that you can express a number as a product of two factors.
10 is divisible by 1,2, 5, and 10. |
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15 is divisible by ________________. |
14 is divisible by ________________. |
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11 is divisible by ________________. |
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3. Use the previous exercise as a help and make a divisibility list of numbers between 1 and 20. Circle every number that is divisible only by 1 and the number itself. Such numbers are called prime numbers. (Usually 1 is excluded and is not counted as a prime number.)
| number | divisible by: (divisors) |
number |
divisible by: |
number |
divisible by: |
number |
divisible by: |
| 1 | 1 | 6 | 11 | 16 | |||
| 2 | 7 | 12 | 17 | ||||
| 5 | 10 |
1, 2, 5, 10 |
15 | 20 |
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Some numbers only have two divisors: 1 and the number itself. Such numbers are called prime numbers. 11 is one of them. Earlier we found that prime numbers less than 20 are 2, 3, 5, 7, 11, 13, 17, and 19. 1 is usually not counted as a prime number. |
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1. Fill the table and circle each prime number between 20 and 30.
| number | divisible by: (divisors) |
number |
divisible
by: |
| 21 | 26 | ||
| 22 | 27 | ||
| 23 | 28 | ||
| 24 | 29 | ||
| 25 | 30 |
2. Factor the following numbers so the factors are prime numbers.
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18
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6
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14
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| 25 / \
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33 / \
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15 / \
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| Prime numbers are like building blocks of all numbers. They are the
first and foremost, and other numbers are 'built' from them. ALL numbers
can be factored down so the factors are just prime numbers. That is sort
of amazing - think about it! For example, try these bigger numbers:
Does it matter how you start your factorization? Try and see.
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We can do the factoring process backwards, too. Let's start with the
building blocks and build numbers:
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3. Build numbers from primes.
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2 × 5 × 11 \ / | |
3 × 2 × 2 × 2 \ / \ / |
2 × 3 × 7 |
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Continue to Sieve of Eratosthenes
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