Number Factors

Hi. In this math post, the focus is on number factors. This topic is useful for those at around grades six to ten. Number factors are helpful for division, and the algebra method of factoring.

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Table Of Contents

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• What Is A Factor?

• Examples of Number Factors

• Prime Numbers & Prime Factorization

• Practice Problems

• Answers

• References

What Is A Factor?

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A number factor is a positive whole number which (exactly) divides into another whole number with a zero remainder. In other words, a whole number divided by a factor gives another whole number. As an example, any even number can be divided by 2 with zero remainder.

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Examples of Number Factors

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Here are some examples.

The number 6 has factors of 1, 2, 3 and 6 itself. These factors divide into 6 exactly since 6 ÷ 1 = 6, 6 ÷ 2 = 3, 6 ÷ 3 = 2, and 6 ÷ 6 = 1.

The number 15 has factors of 1, 3, 5, and 15 itself. We can have 1 × 15 = 15, and 3 × 5 = 15. Alternatively, we can show that 15 ÷ 1 = 15, 15 ÷ 3 = 5, 15 ÷ 15 = 1, and 15 ÷ 5 = 3.

Factors are not restricted to numbers. We can use variables such as x. As an example, factors of are 1, x and itself.

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Prime Numbers

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If a whole positive number has two factors which are 1 and itself, this number is considered as a prime number. Examples of prime numbers include 2, 3, 5, 7, 11, 13, and 29.

Prime Factorization

Any positive whole number greater than one has number factors which are prime numbers. As an example, the number 42 can be written as:

42 = 2 x 3 x 7

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Practice Problems

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1. What are the factors of the number 12?

2. What are the factors of the number 49?

3. What are the factors of the number 35?

4. Is 31 a prime number? Why?

5. What are the factors of

6. What are the factors of

7. Find the prime factors of the number 60.

Answers

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1. 1, 2, 3, 4, 6 and 12

2. 1, 7, 49

3. 1, 5, 7, 35

4. The factors of 31 are 1, and 31 itself. It is a prime number.

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References

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• https://www.mathsisfun.com/prime-factorization.html

• https://www.mathsisfun.com/prime_numbers.html

• http://www.purplemath.com/modules/factnumb.htm

I used http://www.quicklatex.com/ and http://math.typeit.org/ for math text/images.