Finding common factors is like being a detective ๐ต๏ธโโ๏ธ. You're looking for the numbers that can divide evenly into two or more other numbers. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 18 are 1, 2, 3, 6, 9, and 18. The common factors of 12 and 18 are the numbers that appear in both lists: 1, 2, 3, and 6.
These worksheets will give you practice finding common factors, so you'll become super confident. Knowing common factors is important because it helps simplify fractions and solve other math problems. So, let's get started and make math fun! ๐
Match the term with its definition:
| Term | Definition |
|---|---|
| 1. Factor | A. A number that divides evenly into another number. |
| 2. Common Factor | B. The greatest factor that two or more numbers share. |
| 3. Multiple | C. A number obtained by multiplying a number by an integer. |
| 4. Prime Number | D. A whole number greater than 1 that has only two factors: 1 and itself. |
| 5. Greatest Common Factor (GCF) | E. A factor that two or more numbers share. |
(Answers: 1-A, 2-E, 3-C, 4-D, 5-B)
The __________ of a number are the numbers that divide evenly into it. A __________ __________ is a factor that is shared by two or more numbers. The largest of these shared factors is called the __________ __________ __________ (GCF). For example, the factors of 10 are 1, 2, 5, and 10. The factors of 15 are 1, 3, 5, and 15. The common factors of 10 and 15 are __________ and __________. The GCF of 10 and 15 is __________.
(Answers: factors, common factor, greatest common factor, 1, 5, 5)
Explain in your own words why finding the greatest common factor (GCF) is useful in simplifying fractions. Give an example.
(Example Answer: Finding the GCF helps simplify fractions because you can divide both the numerator and the denominator by the GCF, resulting in a fraction in its simplest form. For example, to simplify the fraction \(\frac{8}{12}\), you find that the GCF of 8 and 12 is 4. Dividing both 8 and 12 by 4 gives you \(\frac{2}{3}\), which is the simplified form of \(\frac{8}{12}\).)
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