THE TRANSITION LINE // FIELD NOTES // STOP 05
Factors, primes, and divisibility
Field Book
Lessons 17 to 20
Method
Pencil and paper. Calculators never.
Drill duty posts at the yard. Facts without hesitation keep the Line moving. Factors pair off, multiples skip-count, primes refuse to break, the greatest common factor gets hunted by list, the divisibility rules read a number without dividing it, and a fraction of a number runs in two steps.
What you have to be able to do
- List factors in pairs and multiples in order
- Tell prime from composite and find a GCF
- Apply the divisibility rules for 2, 3, 5, 6, 9, and 10
- Take any fraction of a number
The procedures
Factors and multiplesField Book Lesson 17
- List factors in pairs until the pairs meet in the middle.
- Multiples: skip-count the number as far as needed.
Prime, composite, and the GCFField Book Lesson 18
- A composite breaks into two smaller factors. A prime does not.
- GCF: list each number's factors, keep the common ones, take the largest.
Divisibility rulesField Book Lesson 19
- 2, 5, and 10 read the last digit.
- 3 and 9 read the sum of the digits. 6 needs both the 2 rule and the 3 rule.
Fraction of a numberField Book Lesson 20
- Divide the number by the bottom.
- Multiply that answer by the top.
Worked: GCF at the depot
- 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
- Common: 1, 2, 3, 4, 6, 12. The GCF is 12.
Worked: three eighths of the load
- 38 of 56 barrels: 56 ÷ 8 = 7, then 7 · 3 = 21.
- 21 barrels.
Terms on the record
| Term | Meaning |
|---|
| factor | a number that divides evenly into a given number |
| multiple | a number the given number multiplies into evenly |
| prime number | a number that cannot break into two smaller factors |
| composite number | a number that can break into two smaller factors |
| greatest common factor | the largest number dividing evenly into two or more numbers |