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The factor tree is used to find the prime factorisation of the numbers. The greatest common factor is then the product of every common prime across the numbers; if a prime occurs more than once in all the numbers, then it is included more than once.
For example the gcf(60, 72):
The trees are written with branches that multiply to the numbers from which they fork:
_________60______________________________72_________________
________/___\____________________________/___\________________
_______/_____\__________________________/_____\_______________
______4_____15_______________________8_______9______________
_____/_\____/__\______________________/_\______/_\_____________
____2__2__3___3___________________4___2____3__3____________
___________________________________/_\________________________
__________________________________2__2_______________________
(Note that 60 = 4 × 15, 8 = 4 × 2, etc. The actual factorisations down the tree do not matter as long as each number is split into a factor pair. I've had to use the underscore character (_) to keep the columns aligned as spaces get trimmed in answers - think of them like lines on a piece of paper.)
When the number is a prime, it is the end of a branch. The prime factorisation of the number is then read from the ends of all the branches:
60 = (2) × (2) × (3) × 5
72 = (2) × (2) × 2 × (3) × 3
The common primes I have enclosed in parentheses and are 2 × 2 × 3 = 12.
Thus gcf(60, 72) = 12.
If the prime factorisation is written in power format, the gcf is the product of the common primes to their lowest power. For the above, this becomes:
60 = 2² × 3 × 5
72 = 2³ × 3²
The common primes are 2 and 3. The lowest power of 2 is 2² and the lowest power of 3 is 3¹ = 3. Thus gcf = 2² × 3 = 12.
The factor tree is just a way of notating the process of finding the prime factorization.
Example: 30 and 42
30
15,2
5,3,2
42
21,2
7,3,2
2 x 3 x 5 = 30
2 x 3 x 7 = 42
Select the common factors.
2 x 3 = 6, the GCF
Example: 30 and 42
30
15,2
5,3,2
2 x 3 x 5 = 30
42
21,2
7,3,2
2 x 3 x 7 = 42
Select the common factors.
2 x 3 = 6, the GCF
Factor trees give you the prime factorization.
Comparing prime factorizations gives you the GCF.
Example: 30 and 42
30
15,2
5,3,2
42
21,2
7,3,2
2 x 3 x 5 = 30
2 x 3 x 7 = 42
Select the common factors.
2 x 3 = 6, the GCF
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What is the greates common factor of the numbers 155 using prime factorization?
You need at least two numbers to find a GCF.
How do you find the greatest common factor of 10 and 15 using a division ladder?
15 5,3 10 5,2 The GCF is 5.
What is the greatest common factor of 144 and 36 using the factor tree method?
Trees aren't necessary. Since 36 is a factor of 144, it is automatically the GCF. But if you insist... 144 72,2 36,2,2 18,2,2,2 9,2,2,2,2 3,3,2,2,2,2 36 18,2 9,2,2 3,3,2,2
What is the greatist common factor of 10?
You need at least two numbers to find a GCF.
What is the GCF of 28 using prime factors?
There cannot be a greatest common factor (GCF) of just one number. To be common there need to be at least two numbers. If you find all the factors of two or more numbers, and you find some factors are the same ("common"), then the largest of those common factors is the Greatest Common Factor.
How do you simplify fractions using the factor tree?
To simplify fractions, it is necessary to divide the numerator and the denominator by their GCF. You can find their GCF by comparing their prime factorizations. You can find their prime factorizations through the use of factor trees.
What is the greatest common factor of a factor tree?
You need at least two factor trees to find a GCF.
What is the GCF of 9 and 54 with factor trees?
GCF=6
How do you Simplify the fraction 150 over 225 with factor trees?
The factor trees find the prime factorizations. The prime factorizations find the GCF. The GCF simplifies the fraction. 150 75,2 25,3,2 5,5,3,2 225 75,3 25,3,3 5,5,3,3 The GCF is 75 150/225 = 2/3
What is the GCF of 42 using a factor tree?
42 21,2 7,3,2 You need at least two numbers to find a GCF.
How do you find GCF and LCM?
To find the GCF and the LCM you have to first at least try to use prime factorization. So use factor trees. Or for the LCM find th least common multiples of the number.
Why do factor trees always come up with the GCF?
Factor trees come up with prime factorizations. When you compare one prime factorization with another, you can come up with a GCF.
How do you find the gcf of 36 and 45 using a factor tree?
Using ANY METHOD find the GCF of 30 & 25: The GCF of 30 & 25 =
How do you find the greatest common factor of 32 and 40 using factor trees?
32 16,2 8,2,2 4,2,2,2 2,2,2,2,2 40 20,2 10,2,2 5,2,2,2 Select the common factors. 2 x 2 x 2 = 8, the GCF
What is the gcf of 13 and 65?
its 13 but to get it u can do factor trees that's how i do it
How do you find the greatest common factor of 12 18 and 24 using short division?
The GCF is 6.
How do you yuse factor trees to find the gcf two numbers?
Example: 30 and 42 30 15,2 5,3,2 42 21,2 7,3,2 2 x 3 = 6, the GCF
