Download Fifth Grade Study Sheet

Fifth Grade Study Sheet
Number Theory
Whole numbers (that’s a number that is not a fraction, decimal or percent) can be
classified as prime or composite.
A prime number has only two divisors or factors, 1 and the number itself. For example,
the number 2 is prime because it’s only factors are and itself, 2 (1 x 2). The number 3 is
also a prime number because its only factors are 1 and 3 (1 x 3). Here’s a list of the first
few prime numbers: 2, 3, 5, 7, 11, 13, 17, 23 … All prime numbers are odd (except for
the numbers 2).
To find if a number is prime, think: Can the number be divided by a number other than 1
and itself?
A composite number has more than two factors. The number 4 is composite because it
has three factors; 1, 2 and 4 (1 x 4, 2 x 2). Here’s a list of the first few composite
numbers: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18 … All even numbers are composite (except for
the number 2).
To find all the factors of a number, look for factor pairs. A factor pair is a pair of whole
numbers (that’s two numbers) whose product is the number. For example, the factor pairs
for 12 are: 1 and 12 (1 x 2), 2 and 6 (2 x 6), 3 and 4 (3 x 4).
A factor rainbow can help you organize the factor pairs: Let’s find the factor pairs for 24.
1. Start with the number 1 on the left side of your paper and write its pair on the
opposite end of the pair.
1
24
2. Next write the number 2 next to the number one and 12 next to the 24.
1, 2
12, 24
3. Continue in order until you’ve matched the pairs of factors.
1, 2, 3, 4, 6, 8, 12, 24
*Notice that 24 is the largest factor and 1 is the smallest factor.*
Do you remember how to count by 2’s, 5’s and 10? Well, when you count by 2’s, 5’s or
10’s you are saying the multiples of that number.
Count by 2’s … 2, 4, 6, 8, 10… These are the multiples of 2. The multiples of 7 are 7, 14,
21, 28, 35, 42, 49 …
What are the multiples of 3, 4 and 6?
To find the Greatest Common Factor (GCF) of a set of numbers you will first list all
the factors of the given numbers. For example,
8: 1, 2, 4, 8
32: 1, 2, 4, 8, 16, 32
Once you have listed all the factors you will find which factors they share in common.
For 8 and 32 the common factors are 1, 2, 4 and 8. The GCF is the factor they share in
common with the greatest value, 8.
Prime Factorization is used to break down numbers to its factors. Keep breaking
numbers down to their factors until you get only prime numbers. Write the prime factors
on the line below each problem.
Example;
24
6
4
2
3
2
Prime factors of 24 = 2 x 2 x 2 x 3
2