Before learning factor tree online, we'll learn important terms related with factor tree. Those terms are given below:
Factor: A factor of a number is the exact divisor of that number. In other words, a factor of the number divides the number leaving remainder 0.
We know that 15 = 1 x 15 and 15 = 3 x 5. This shows that 1, 3, 5 and 15 exactly divides 15. Therefore, 1, 3, 5 and 15 are all factors of 15.
Prime Number: Each of the numbers which has exactly two factors, namely, 1 and itself, is called a Prime Number. For example: 2, 3, 5,11, 13 etc.
Prime Factor: A factor of a given number is called a prime factor if this factor is a prime number. A prime factor cannot be factored further.Example: 2 and 3 are prime factors of 12 while 4, 6 and 12 are not.
Prime factorization : To express a given number as a product of prime factors is called Prime Factorization or complete factorization of the given number.
Example: 36 = 2 x 2 x 3 x 3, 45 = 3 x 3 x 5 etc.
Factor Tree: A diagram that shows the prime factors of a number is known as Factor tree. A factor tree contains all the prime factors of a given number.
Process to make a factor tree online
Start with the number.
Factor: A factor of a number is the exact divisor of that number. In other words, a factor of the number divides the number leaving remainder 0.
We know that 15 = 1 x 15 and 15 = 3 x 5. This shows that 1, 3, 5 and 15 exactly divides 15. Therefore, 1, 3, 5 and 15 are all factors of 15.
Prime Number: Each of the numbers which has exactly two factors, namely, 1 and itself, is called a Prime Number. For example: 2, 3, 5,11, 13 etc.
Prime Factor: A factor of a given number is called a prime factor if this factor is a prime number. A prime factor cannot be factored further.Example: 2 and 3 are prime factors of 12 while 4, 6 and 12 are not.
Prime factorization : To express a given number as a product of prime factors is called Prime Factorization or complete factorization of the given number.
Example: 36 = 2 x 2 x 3 x 3, 45 = 3 x 3 x 5 etc.
Factor Tree: A diagram that shows the prime factors of a number is known as Factor tree. A factor tree contains all the prime factors of a given number.
Process to make a factor tree online
Start with the number.
- Make branches of factors - numbers that multiply to give you the original number
- Keep reducing each factor to its lowest possible prime factors.
- When we have all the prime factors identified, re-arrange them from least to greatest.
- Re-write them as exponents.
Illustration: Lets see the factor tree online preparation of 36 and 180 in the figure below:
1) Factor tree of 36:
2. Factor tree of 180
Uses Of Factor Tree online
1. Factor Tree online is used to find the GCF or HCF
Example: Find the greatest common factor of 18 and 54.using factor tree
18
3 x 6
3 x (2x3)
The prime factors of 18 are 2, 3, and 3.
54
6 x 9
(2x3) x (3x3)
The prime factors of 54 are 2, 3, 3, and 3.
The prime factors that 18 and 54 have in common are 2, 3 and 3, so the greatest common factor is 2 x 3 x 3 = 18.
2. Factor Tree is used to find the LCM or LCD
Example: Find the LCM of 12 and 36 using factor tree
Step 1: Find the Prime factors for
12 = 2 x 2 x 3
36 = 2 x 2 x 3 x 3
Step 2: Multiply each prime factor the greatest number of times it appears in any one factorization.
The most number of times 2 appears in either factorization is twice. The most number of times 3 appears in either factorization is twice.
Thus, LCM = 2 x 2 x 3 x 3 = 36
1) Factor tree of 36:
2. Factor tree of 180
Uses Of Factor Tree online
1. Factor Tree online is used to find the GCF or HCF
Example: Find the greatest common factor of 18 and 54.using factor tree
18
3 x 6
3 x (2x3)
The prime factors of 18 are 2, 3, and 3.
54
6 x 9
(2x3) x (3x3)
The prime factors of 54 are 2, 3, 3, and 3.
The prime factors that 18 and 54 have in common are 2, 3 and 3, so the greatest common factor is 2 x 3 x 3 = 18.
2. Factor Tree is used to find the LCM or LCD
Example: Find the LCM of 12 and 36 using factor tree
Step 1: Find the Prime factors for
12 = 2 x 2 x 3
36 = 2 x 2 x 3 x 3
Step 2: Multiply each prime factor the greatest number of times it appears in any one factorization.
The most number of times 2 appears in either factorization is twice. The most number of times 3 appears in either factorization is twice.
Thus, LCM = 2 x 2 x 3 x 3 = 36
No comments:
Post a Comment