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Maths

Factor and Factor Tree

Table of Contents

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What are Factors?

Factor is a basic Mathematical concept taught to primary-grade students in schools. In simple terms, a factor of a number can be divided by the given number evenly without leaving any remainder. There are two popular methods of calculating the factor of a number, i.e., the multiplication method and the division method. Let’s understand how to calculate factors with one example:

Example:
Let’s find the factors of 8 by using the multiplication method.

Answer:
Factors of 8 are the numbers that will be divided by the number 8 evenly. We will find the factors of 8 by using the division method. For this method, we will divide 8 with a sequence of numbers. The numbers that will get divided by 8 completely will be termed as the factors of 8.

8 ÷ 1 = 8 (Remainder = 0)
8 ÷ 2 = 4 (Remainder = 0)
8 ÷ 3 = 2 (Remainder = 2)
8 ÷ 4 = 2 (Remainder = 0)
8 ÷ 5 = 1 (Remainder = 3)
8 ÷ 6 = 1 (Remainder = 2)
8 ÷ 7 = 1 (Remainder = 1)
8 ÷ 8 = 1 (Remainder = 0)

From the above, we can see that the numbers 1, 2, 4, and 8 when divided by 8 leave the remainder 0. Hence, 1, 2, 4, and 8 are the factors of 8.

What is a Factor Tree?

Factor tree can be defined as a way of expressing the factors of a number, specifically the prime factorization of a number. The factors are represented as the branches of a tree and at the end of the branch is a prime number that cannot be spilt further. Let’s understand this concept with an example.

Example:
Factor tree of 32.

Answer:
The calculation of a factor tree starts by placing the given number at the top of the tree and the set of pair factors will be written as branches of the trees which will be continued till we get a prime number. Now, let’s see the steps to calculate the factor tree of 32.

  • Step 1: First place 32 at the top of the factor tree and write down 32 in pairs, that is, 2 and 16.
  • Step 2: Since 2 is a prime number, we can no longer separate it. Let us circle 2 and move on to the next number. We will now divide 16 into 2 and 8.
  • Step 3: As we can see, 2 is a prime number but 8 is not, so we will split 8 into 2 and 4.
  • Step 4: Now again, we will leave 2 as it is because it is a prime number, but we will break 4 into 2 and 2.
  • Step 5: We can see that 2 is a prime number. The branches in the factor tree will now be all the prime numbers. Hence, circling all the branches, 25 or 2 X 2 X 2 X 2 X 2= 32, which are 32 prime factors.