Here we are going to discuss, what are the factors of 92 and how many factors 92 has and what are the factors of 92 in pairs. Here are some methods, showing how to find the factors of 92.
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 2 to 46, it gives 92. Here 2 and 46 are positive factors of 92 or we multiply -4 to -23, it gives 92. So -4 and -23 are negative factors of 92.
What are the Factors of 92?
Since factors of 92 are the numbers, which divides 92 completely without leaving the remainder. So here we are
going to divide 92 by all numbers up to 92. 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 23 appears in column ‘A’, which has already been come in column ‘B’.
Hence, positive factors of 92 in above table are : 1, 2, 4, 23, 46, 92
Similarly, negative factors of 92 are : -1, -2, -4, -23, -46, -92
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 92
As we saw in the above table, 1 multiply by 92 gives 92. So (1, 92) or (92, 1) is a factor pair of 92.
Similarly, (2, 46), (4, 23) are another factor pairs of 92.
In example of 49 ; (1, 49) or (49, 1) and (7, 7) are factor pairs.
Methods of Prime Factors of 92
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 92
In the above example of 92
Step 1 : First of all, we divide 92 by the smallest prime number i.e. 2. It gives 46 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 46 by a prime number i.e. 2, it gives 23 as a quotient and the remainder is zero.
Step 3 : Since 23 is a prime number, hence it will divide by itself only.
Hence, 92 = 2 x 2 x 23. So 92 has two prime factors i.e. 2 and 23.
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 92
In the factor tree method, we can initiate the tree by choosing any two factors. Here we choose 4 and 23 as factors of 92.
Further, we have to divide these nodes ( 4 & 23). Since 23 is a prime number and can’t be split anymore. So we split 4 into two factors 2 and 2.
We got 2, 2 and 23 as end nodes.
Since both 2 and 23 are prime numbers and can not be further split.
Hence, we got 2 and 23 unique nodes.
Note:- The Factor Tree may be made 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 92 = 2 x 2 x 23 = 22 x 23 means 2 to the power 2 multiply 23 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 92.
Try another number 52 for factors.