Prime Factorization
What does it mean to find the prime factorization of a number?
The prime factorization of a number is when we have reduced all of its factors into prime numbers and cannot be broken down any further.
How do you know when you've completely factored a number?
When going in order from smallest to largest divisors, you know you have found the same factors when you repeat a combination you've already found. Like 2*9 then you find 9*2
What does LCM stand for?
Lowest common multiple. The smallest number a set of numbers both multiply too.
What does GCF mean?
Greatest Common Factor. This is the largest number that divides both numbers in the set
How can you tell the difference between LCM and GCF in a word problem?
LCM is trying to find the common number that you would have to get for each, GCF is trying to divide into an equal number of groups with no leftovers.
What is the prime factorization of 32?
32=2*2*2*2*2 or 2^5
What are all of the factors of 12? Put them in order from least to greatest
The factors of 12 are 1,2,3,4,6,12
What's the LCM of 6 and 8?
8=2^3, 6=2*3
LCM=2*2*2*3=24
What's the GCF of 6 and 18?
GCF=6
Jenny is a dental sales representative who wants to distribute 24 brochures and 48 pamphlets to local dental offices. She wants to deliver the same combination of brochures and pamphlets to each office, without having any materials left over. What is the greatest number of dental offices Jenny can distribute materials to?
GCF = 24
What is the prime factorization of 48?
48=2*2*2*2*3 or 2^4*3
What are all of the factors of 30? Put them in order from least to greatest
The factors of 30 are 1,2,3,5,6,10,15,30
What's the LCM of 10 and 4?
10=2*5, 4=2*2
LCM=2*2*5=20
What's the GCF of 15 and 24?
GCF=3
Jackie notices an identical number of two types of insects in her neighborhood: butterflies and fireflies. She always seems to observe butterflies in groups of 9 and fireflies in groups of 2. What is the smallest number of butterflies that she could have seen?
LCM=18
What is the prime factorization of 75?
75=3*5*5 or 3*5^2
What are all of the factors of 45? Put them in order from least to greatest.
he factors of 45 are 1,3,5,9,15,45
What's the LCM of 21 and 9?
21=3*7, 9=3*3
LCM=3*3*7=63
What's the GCF of 24 and 60?
GCF=12
Jada is making a scrapbook using 46 photos and 23 newspaper clippings. She wants all the pages to be set up in the same way, with the same combination of photos and newspaper clippings on every page. She also wants to make sure that no items are left over. What is the greatest number of scrapbook pages Jada can create?
GCF = 23
What is the prime factorization of 1500?
1500=2*2*3*5*5*5 or 2^2*3*5^3
What are all of the factors of 100? Put them in order from least to greatest
The factors of 100 are 1,2,4,5,10,20,25,50,100
What's the LCM of 24 and 20?
24=2*2*2*3, 20=2*2*5
LCM=2*2*2*3*5=120
What's the GCF of 36 and 81?
GCF=9
Mitchell is buying flower bulbs for his garden. He wants to buy the same number of tulips and daffodils. If tulip bulbs come in packs of 4 and daffodil bulbs come in packs of 9, what is the least number of each type of bulb Mitchell will need to buy?
LCM=36