A factor tree shows the prime factors of a composite number in a “tree-like” form. Drawing factor trees is a good way of doing prime factorization. You can make different factor trees to find the same prime factorization. Look at the two examples below.
What is the prime factor tree for 36?
Prime Factorization of 36 by Factor Tree Method A factor tree is not unique for a given number. Instead of expressing 36 as 2 × 18, we can express 36 as 6 × 6. Prime factorization of 36 using factor tree method is 2 × 2 × 3 × 3 = 2² × 3².
What is the factor tree of 69?
Factor Tree of 69 to Calculate the Factors
| 69 | |
|---|---|
| 3 | 23 |
How are factor trees used to calculate prime factorization?
The factor tree method is quite flexible – at each branch you can break the number into any factors until you reach the prime factors. Although the order of the factors may be different because we can start with different pairs of factors, every factor tree of 36 has the same prime factorization.
Is the prime factorization of 36 the same for all factor trees?
Although the order of the factors may be different because we can start with different pairs of factors, every factor tree of 36 has the same prime factorization. We can also use exponents to write the prime factorization. 36 = 2 2 × 3 2.
Is the factorization of 3 a prime number?
And 3 is a prime number, so we have the answer: As you can see, every factor is a prime number, so the answer must be right. Note: 12 = 2 × 2 × 3 can also be written using exponents as 12 = 22 × 3 Example 2: What is the prime factorization of 147 ? Can we divide 147 exactly by 2? No it can’t. The answer should be a whole number, and 73½ is not.
How to find the prime factors of two numbers?
Step 1: Find the prime factorisation of both the numbers. Step 2: Find the common prime factors of the given numbers. Common factors = 2, 2, 2, 3 Step 3: Multiply all the common factors to find out the HCF. ∴ HCF = 2 × 2 × 2 × 3 = 24 The HCF of two or more numbers is the greatest common factor of all the given numbers.
