Transcript Greatest Common Factor

the largest number that can divide
into all of the numbers.
Find the GCF of 42 and 60.
Write the prime factorization of
each number.
42 2
21 3
7 7
1
60
30
15
5
2
2
3
5
1
What prime factors do the numbers have in common?
Multiply those numbers with the lowest exponents .
The GCF is 2 x 3 = 6
6 is the largest number that can go into 42 and 60!
Step 1:
Make a “TChart” for both
numbers.
Step 2:
Look for
common factors
between both
numbers.
Step 3:
Circle the
greatest factor
that both
numbers have in
common.
Step 4:
This is the GCF.
Find the Greatest Common Factor
(GCF) of 16 and 24.
16
1 × 16
2 ×8
4 ×4
24
1 × 24
2 × 12
3 ×8
4 ×6
The GCF of 16 and 24 is 8
© 2007 M. Tallman
 Find the GCF of
 12 and
18
 18 and 27
 24 and 30
 36 and 45
 24 and 36
 16, 32 and 40
 18,27 and 36
Find the HCF of :
1)
2)
3)
4)
5)
2x3x5 and 2x3x7
2x3x5x7 and 2x2x3x11
2x2x3x5 and 2x2x3x11
2x2x2x5x7 and 2x2x2x5x11
2x2x2x7x7 and 2x2x2x7x11
Samantha has two pieces of cloth. One piece is 72 inches wide and the other piece is 90
inches wide. She wants to cut both pieces into strips of equal width that are as wide as
possible. How wide should she cut the strips?
2 l 72
2 l 36
2 l 18
3l9
3l3
1
2 l 90
3 l 45
3 l 15
5l5
1
72 = 2 x 2 x 2 x 3 x 3
90 = 2 x 3 x 3 x 5
GCF = 2 x 3 x 3 = 18
Samantha should cut each piece to be 18 inches wide
1. Mrs. Evans has 120 crayons and 30 pieces of paper to give
to her students. What is the largest # of students she can
have in her class so that each student gets equal # of
crayons and equal # of paper.
2. I am planting 50 apple trees and 30 peach trees. I want the
same number and type of trees per row. What is the
maximum number of trees I can plant per row?
 the smallest number that is common
between two lists of multiples.
42 2
21 3
7 7
1
60
30
15
5
2
2
3
5
1
Write the common and non common factors
with the greatest exponents
The LCM of 42 and 60 is 420.
Find the least common multiple (LCM).
Method 2: Use a list.
3, 4, and 9
3: 3, 6, 9, 12, 15, 18, 21, 24,
27, 30, 33, 36, . . .
List multiples of 3, 4, and
9.
4: 4, 8, 12, 16, 20, 24, 28, 32,
36, …
Find the smallest number
that is in all the lists.
9: 9, 18, 27, 36, 45, . . .
The least common multiple of 3, 4, and 9 is 36.
Find the LCM of the following
1.
2.
3.
4.
5.
2 and 5
3 and 8
2, 3 and 4
3 and 9
2,4 and 6
1. 2x5 and 5x5
2. 2x2x3 and 2x2x5
 3. 2x2x3 and 2x7
4.2x2x2 and 2x7
5. 2x2x5 and 5x5
 Ben exercises every 12 days and Isabel every 8 days. Ben and
Isabel both exercised today. How many days will it be until
they exercise together again?
2 l 12
2l6
3l3
1
12 = 2 x 2 x 3
8=2x2x2
2l8
2l4
2l2
1
LCM = 2 x 2 x 2 x 3 = 24
Ben and Isabel would exercise on the same day every 24 days.
1.Two bikers are riding a circular path. The first rider completes a
round in 12 minutes. The second rider completes a round in 18
minutes. If they both started at the same place and time and go
in the same direction, after how many minutes will they meet
again at the starting point?
2. Sean has 8-inch pieces of toy train track and Ruth has 18-inch
pieces of train track. How many of each piece would each child
need to build tracks that are equal in length?