Number Theory Properties Of Integers Worksheet (Page 2 of 2) in pdf

Number Theory Properties Of Integers Worksheet Page 2

Greatest Common Factor

Method 1: Perform the prime factorization for each integer.

Prime factorization is:

360

Prime factorization is:

Circle any factor(s) that are common to both. The greatest common factor of 75, 360 is:

Method 2: Write out all the factors of each integer as a list, from smallest to largest.

Factors are: 1, 3, 5, 25, 75

360

Factors are: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360

Go through the list until you find the largest common factor.

Exercise 2: Find the greatest common factor of the following pairs of integers:

40, 48

10, 20

28, 42

360, 270

75, 100

24, 36

Least Common Multiple

Method 1: List the multiples of both numbers until you reach a common multiple:

15, 30, 45, 60, 75. …

12, 24, 36, 48, 60, 72, …

The least common multiple of 15 and 12 is 60.

Method 2: (using primes)

Take one of these numbers, say 15, circle the prime factorization. On the other integer, score out any

common factor. Circle the remaining factors.

The least common multiple of 15 and 12 is

Exercise 3: Find the least common multiple of the pairs of integers in exercise 2.

Number Theory Properties Of Integers Worksheet Page 2