Transcript Greatest Common Factor (GCF) - Iroquois Central School

GREATEST COMMON FACTOR
GCF
Divisibility Rules
2, if it ends in a even number in the ones place (0,2,4,6,8).
Example: 558 because there is a 8 in the ones place
3, if the sum of its digits is divisible by 3.
Example: 81 because 8 + 1 = 9 and 9 is divisible by 3
4, if the last 2 digits are divisible by 4
Example: 124 because 24 is divisible by 4
5, if the ones digit is 5 or 0.
Example: 1125 because there is a 5 in the ones place
Divisibility Rules
6, if the number is divisible by both 2 and 3
Example: 48
There is an 8 in the ones place so it is divisible by 2
8 + 4 = 12 and 12 is divisible by 3
8, if the last 3 digits are divisible by 8
Example: 1240 because 240 is divisible by 8
9, if the sum of the digits is divisible by 9
Example: 468 because 4 + 6 + 8 = 18 and 18 is divisible by 9
10, if the number ends in a zero
Example: 50 because the number ends in zero
Common Factors
DEFINITION: Any integer that can evenly
divide into all the numbers in a given set of
numbers
Example: Find the common factors of 10 and 20 by listing all the
factors.
1, 2, 5, 10
Factors of 10: _____________________________
1, 2, 4, 5, 10, 20
Factors of 20: _____________________________
1, 2, 5, 10
Common Factors of 10 and 20: ______________________
Greatest Common Factor
DEFINITION: The largest integer that can
evenly divide into all of the numbers in a set of
numbers.
There are two methods we can use to find the greatest common
factor of two or more numbers…
METHOD 1: MAKE A LIST
List all the factors of each number. Circle the greatest factor that
appears in the lists.
Greatest Common Factor
METHOD 1: MAKE A LIST
List all the factors of each number. Circle the greatest factor that
appears in the lists.
Example 1: Find the greatest common factor of 12 and 18
1, 2, 3, 4, 6, 12
Factors of 12: _____________________________
2, 3, 6, 9, 18
Factors of 18: 1,
_____________________________
Greatest Common Factor of 12 and 18: __
6
Greatest Common Factor
METHOD 1: MAKE A LIST
List all the factors of each number. Circle the greatest factor that
appears in the lists.
Example 2: Find the greatest common factor of 12, 18, and 24
1, 2, 3, 4, 6, 12
Factors of 12: _____________________________
2, 3, 6, 9, 18
Factors of 18: 1,
_____________________________
2, 3, 4, 6, 8, 12, 24
Factors of 24:1,_____________________________
6
Greatest Common Factor of 12, 18, and 24: __
Greatest Common Factor
METHOD 2: Upside Down Cake
Example 1: Find the GCF(12,32)
If you are “stuck”
always start with 2
2
2
Since 3 and 8 share no
common factors, stop here!
12
32
6
16
3
8
Multiply the circled numbers
Greatest Common Factor of 12 and 32: 4
__
Greatest Common Factor
METHOD 2: Upside Down Cake
Example 1: Find the GCF(32,96)
If you are “stuck”
always start with 2
2
32
2
Since one of your numbers is
now 1, stop here!
96
16
2 8
48
24
2 4
12
22
1
6
3
32
Greatest Common Factor of 12 and 32: ___
Greatest Common Factor
METHOD 2: Upside Down Cake
Example 2: Find the GCF(30,48,120)
If you are “stuck”
always start with 2
2
If 2 doesn’t work, go on
to the next number
Since your numbers share no
common factors, stop here!
3
30
48
120
15
5
24
8
60
20
6
Greatest Common Factor of 30,48,120: ___
MR. GROVER WANTS TO MAKE
SHELVES FOR HIS GARAGE USING AN
18-FOOT BOARD AND A 36-FOOT
BOARD. HE WILL CUT THE BOARDS
TO MAKE SHELVES OF THE SAME
LENGTH AND WANTS TO USE ALL OF
BOTH BOARDS. FIND THE GREATEST
POSSIBLE LENGTH OF EACH SHELF.
ANSWER 18 FOOT BOARDS
THE SGB REPS ARE MAKING SPIRIT
RIBBONS. BLUE RIBBON COMES IN A
24 INCH SPOOL, RED RIBBON COMES
IN A 30 INCH SPOOL, AND GOLD
RIBBON COMES IN A 36 INCH SPOOL.
THE SGB REPS WANT TO CUT STRIPS
OF EQUAL LENGTH, USING THE
ENTIRE SPOOL OF EACH RIBBON.
WHAT IS THE LENGTH OF GREATEST
PIECE OF RIBBON THAT CAN BE CUT
FROM EACH SPOOL?
ANSWER 6 INCHES