Factors and prime numbers
Arrange tiles into rectangles: factors are the sides you can make, and primes can only make one long row.
Standards: 4.OA.B.4
1Wonder
A gardener has 12 tomato plants and wants to plant them in neat rows, with the same number in every row. How many different ways can she do it? With 13 plants, she has a problem. Why?
2Explore
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Turn your phone sideways, or open this lesson on a tablet or computer. The explanation and quiz below work here.
- Make 12 tiles. Which row lengths make a perfect rectangle with nothing left over?
- Try 13. Can you find any rectangle apart from one long row?
- Turn on Show every rectangle. Which numbers up to 20 have only one rectangle?
- Which number up to 36 has the most rectangles?
3Explain
Factors are rectangle sides
12 tiles can make a 3 × 4, a 2 × 6 or a 1 × 12 rectangle. The side lengths 1, 2, 3, 4, 6 and 12 are the factors of 12: they divide 12 with nothing left over.
A factor of n divides n with nothing left over: it is a side of a rectangle made of n tiles. A prime has exactly two factors, 1 and itself: it only makes a single row. Every whole number above 1 is a product of primes.
4Practice
How many factors does 18 have?
5Recap
- Factors of a number divide it exactly; they are the side lengths of its rectangles.
- Factors come in pairs that multiply to the number.
- A prime has exactly two factors: 1 and itself. 1 is not prime; 2 is the only even prime.
- Every whole number above 1 is a product of primes.