Download handout

Algebra I –Wilsen
Unit 5: Exponents
Day Eight
BLOCK 2
Divisibility Rules: KNOW THESE!!!
If the last digit of a number is even (0, 2, 4, 6, 8), it is divisible by 2.
Circle the following that are divisible by 2:
60
49
72
555
767
1170
If the sum of the digits is divisible by 3, then the number itself is
divisible by 3.
Circle the following that are divisible by 3:
60
49
72
555
767
1170
If the last digit of a number is a 0 or 5, then it is divisible by 5.
Circle the following that are divisible by 5:
60
49
72
555
767
1170
You try…
Each number is divisible by which of the following numbers: 2, 3, 5?
319
411
455
414
382
256
Finding the Factors of a Number
The factors of a number are all the whole numbers (not decimals) that you can multiply
together to get that number. Think of them as occurring in PAIRS.
Example 1
The factors of 10 are
_____ and _____
_____ and _____
The factors of 12 are
_____ and _____
_____ and _____
The factors of 60 are
_____ and _____
_____ and _____
_____ and _____
_____ and _____
_____ and _____
_____ and _____
You try…
Find all the pairs of factors for the following numbers:
14
20
30
32
Prime Factorization of a Number
It’s also going to be useful to find all of the PRIME factors. That means that you’re
looking for the LOWEST factors. Here’s what this looks like, using a PRIME FACTOR
TREE.
Example 2
The prime POWER factorization
of 10 is:
The prime POWER factorization
of 12 is:
You try…
Find the prime POWER factorization of the following numbers, using factor trees.
(a)
25
(b)
70
(c)
120
Finding the Greatest Common Factor of Two Numbers
If you are given two numbers, the GREATEST COMMON FACTOR (GCF) is the biggest
number that goes into BOTH numbers.
What is the largest number that goes into 10 and 12?
What is the Greatest Common Factor (GCF) of 15 and 30?
Sometimes it’s not so easy to find the GCF that goes into both when the numbers are
bigger. In that case, making prime factor trees can help!
Example 3
Find the GCF of 162 and 135, usine prime factor trees.
The prime POWER factorization
of 162 is:
The prime POWER factorization
of 135 is:
The prime factors that they SHARE are ______________
And so the GREATEST COMMON FACTOR (GCF) is __________
Example 4
Find the GCF of 60 and 45 by using PRIME FACTOR TREES.
The prime factors that they SHARE are ______________
And so the GREATEST COMMON FACTOR (GCF) is __________
You try…
1)
Use factor trees to find the greatest common factor of 70 and 42.
2)
Use factor trees to find the greatest common factor of 104 and 78.
3)
Use factor trees to find the greatest common factor of 244 and 240.
4)
Use factor trees to find the greatest common factor of 288 and 240.
Find the GCF of each pair of numbers.
21)
39 and 6
22)
24 and 28
23)
40 and 10
24)
39 and 30
25)
35 and 21
26)
30 and 20
27)
54 and 45
28)
25 and 55
29)
68 and 34
30)
54 and 27
31)
55 and 75
32)
66 and 30
33)
60 and 56
34)
36 and 24