Here we are going to discuss, what are the factors of 63 and how many factors 63 has and what are the factors of 63 in pairs. Here are some methods, showing how to find the factors of 63.
Actually, Factor is a number that divides any number completely without leaving the remainder.
Or simply we can say that if we multiply two whole numbers (positive & negative) and it gives a product. Then the numbers that we multiply, are the factors of the product.
For example, if we multiply 7 to 9, it gives 63. Here 7 and 9 are positive factors of 63 or we multiply -3 to -21, it gives 63. So -3 and -21 are negative factors of 63.
What are the Factors of 63?
Since factors of 63 are the numbers, which divides 63 completely without leaving the remainder. So here we are going to divide 63 by all numbers up to 63. Let’s see the process –
We have to stop the process if any number of column ‘B’ appears in column ‘A’.
Here we stop the division when 9 appears in column ‘A’, which has already been come in column ‘B’.
Hence, positive factors of 63 in above table are : 1, 3, 7, 9, 21, 63
Similarly, negative factors of 63 are : -1, -3, -7, -9, -21, -63
Take another example, Factors of 49
In the above example, no element of Column ‘B’ appears in Column ‘A’, but we stopped the process
when 7 comes, because on dividing by 7, it produces the same number (7 = 7)
So we have to stop the process when any element comes in both columns at the same level.
And this element will consider as a factor.
Note:- This situation occurs with a perfect square number, such as 9, 16, 25, 36, 49 etc.
Factor Pairs of 63
As we saw in the above table, 1 multiply by 63 gives 63. So (1, 63) or (63, 1) is a factor pair of 63.
Similarly, (3, 21), (7, 9) are another factor pairs of 63.
In example of 49 ; (1, 49) or (49, 1) and (7, 7) are factor pairs.
Methods of Prime Factors of 63
Here we will discuss, mainly two methods of factorization to find Prime Factors of any number.
Method #1 (Division Method)
Step 1 : Divide the number by the smallest prime number, which divides the number exactly.
Step 2 : Divide the quotient again by the smallest prime number. If the quotient is not exactly divisible by the
smallest prime number, choose the next smallest prime number.
Step 3 : Repeat Step 2 again and again till the quotient becomes 1.
Step 4 : All the prime numbers used in the above process are the prime factors.
Check : Multiply all the prime factors, the multiplication should be the number itself.
Caution : In this method, only prime numbers will be used to divide.
Take the example of factors of 63
In the above example of 63
Step 1 : First of all, we divide 63 by the smallest prime number i.e. 2. But it doesn’t divide 63 completely. So try next prime number i.e. 3. It gives 21 as quotient and the remainder is zero.
(Note – if remainder will not zero, means doesn’t divide exactly, try next prime number to divide)
Step 2 : Again we have to divide the quotient 21 by a prime number i.e. 3, it gives 7 as a quotient and the remainder is zero.
Step 3 : Since 7 is a prime number, hence it will divide by itself only.
Hence, 63 = 3 x 3 x 7. So 63 has two prime factors i.e. 3 and 7.
Method #2 (Factor Tree Method)
Step 1 : Write a number as the root of the tree
Step 2 : Find the factors of the number, each factor will be considered as root again (now, we got 2 new roots)
Step 3 : Repeat step 2 until we can’t factor anymore (or until we got prime factor)
Step 4 : The end nodes are the prime factors.
Factor Tree of 63
In the factor tree method, we can initiate the tree by choosing any two factors. Here we choose 7 and 9 as factors of 63.
Further, we have to divide these nodes ( 7 & 9). Since 7 is a prime number and can’t be split anymore. So we split 9 into two factors 3 and 3.
We got 3, 3 and 7 as end nodes.
Since both 3 and 7 are prime numbers and cannot be further split.
Hence, we got 3 and 7 unique nodes.
Note:- The Factor Tree may be made of so many types depends upon choosing the initial and middle factors.
In all factor trees, all nodes and unique nodes will be the same, it doesn’t depend on the tree. We can choose any initial nodes and middle nodes.
Number of factors of 92
To find the number of factors, we use Method #1 (Division Method).
In our example, as we saw above 63 = 3 x 3 x 7 = 32 x 7 means 3 to the power 2 multiply 7 to the power 1
Number of factors is = (power + 1)(power + 1)(power + 1)………. = (2 + 1)(1 + 1) = 3 x 2 = 6
if we consider both positive and negative factors, then
total no. of factors = 6 (positive) + 6 (negative) = 12
I hope, this step-by-step tutorial will be helpful to understand the factorization method of 63.
Try another number 92 for factors.