Download 5.1 Number Theory

Chipola College
MGF 1107
5.1 Number Theory__________________________________________________________
Factors – numbers that are multiplied together to obtain a certain product. For example,
factors of 12 are 1, 12, 2, 6, 3, and 4.
Divisible – a number a is divisible by another number b if the remainder is 0 when you
divide b into a. Thus, you can say that b is a divisor of a or another way to
say it is b divides a symbolized as b a .
Prime number – a natural number greater than 1 that has exactly two factors, itself and 1.
Examples/ 2, 3, 5, 7, 11, 13, 17, …
Composite number – a natural number that is divisible by a number other than itself and 1.
Examples/ 4, 6, 8, 9, 10, 12, …
Note: 0 and 1 are neither prime nor composite.
Divisibility Rules
A number is divisible by 2, if the number is even. In other words, ends in 0, 2, 4, 6, or, 8.
A number is divisible by 3, if the sum of the digits is divisible by 3.
A number is divisible by 4, if the number formed by the last 2 digits is divisible by 4.
A number is divisible by 5, if it ends in 0 or 5.
A number is divisible by 6, if it is divisible by 2 AND 3.
A number is divisible by 8, if the number formed by the last 3 digits is divisible by 8.
A number is divisible by 9, if the sum of its digits is divisible by 9.
A number is divisible by 10, if it ends in 0.
Example: Put a check mark in the box if the number is divisible by 2, 3, 4, 5, 6, 8, or 10.
Number
145,860
30,936
2808
423,005
2
3
4
5
6
8
9
10
Prime factorization - the process of breaking down a number into all prime numbers. We
will use the factor tree method and write our answers in terms of bases and exponents.
Write the prime factorization of the following numbers:
1.
2100
2. 12
3. 18
4. 225
5. 525
Greatest Common Divisor (GCD)
To Find the Greatest Common Factor of Two or More Numbers
1. Determine the prime factorization of each number.
2. Write down the common bases with the smallest exponent.
3. Determine the product in step 2.
Find the GCF of:
1. 225 and 525
2. 12 and 18
3. 54 and 90
To Find the Least Common Multiple of Two or More Numbers
1. Determine the prime factorization of each number.
2. Write down all bases with the largest exponent.
3. Determine the product in step 2.
Find the LCM of:
1. 225 and 525
2. 12 and 18
3. 54 and 90
You Try:
Find the GCF and LCM of the following:
1. 20 and 36
2. 120 and 240
3. 18, 78, and 198