Here we are going to discuss, what are the factors of 55 and how many factors 55 has and what are the factor pairs of 55. Here are some methods, showing how to find the factors of 55.
Actually, Factor is a number which divides any number completely without leaving 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 5 to 11, it gives 55. Here 5 and 11 are positive factors of 55 or we multiply -4 to -25, it gives 100. So -4 and -25 are negative factors of 100.
What are the Factors of 55 ?
Since factors of 55 are the numbers, which divides 55 completely without leaving remainder. So here we are
going to divide 55 by all numbers up to 55. 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 11 appears in column ‘A’, which has already been came in column ‘B’.
Hence, all the factors of 55 in above table are : 1, 5, 11, 55
Similarly, negative factors of 55 are : -1, -5, -11, -55
Take another example, Factors of 49
In 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 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 55
As we saw in above table, 1 multiply by 55 gives 55. So (1, 55) or (55, 1) is a factor pair of 55.
Similarly, (5, 11) is another factor pairs of 55.
In example of 49 ; (1, 49) or (49, 1) and (7, 7) are factor pairs.
Methods of Prime Factors of 55
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 quotient is not exactly divisible by the
smallest prime number, choose 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 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 use to divide.
Take example of 55 and 100
In above example of 55,
Step 1 : First of all, we divide 55 by smallest prime number i.e. 2, but it doesn’t completely divides 55. So try next prime numbers, 3 or 5 to divide completely.
(Note – if remainder will not zero, means doesn’t divide exactly, try next prime number to divide)
Step 2: Again we have to divide 55 by a prime number i.e. 5. This time 55 gives 11 as quotient without leaving any reminder.
Step 3: Since 5 and 11 both are prime numbers, hence they will divide by itself only. So 5 and 11 are prime factors.
Hence, 55 = 5 x 11. So 55 has two prime factor i.e. 5 and 11.
In second example of 100
Step 1 : First of all, we divide 100 by smallest prime number i.e. 2 and we got 50 as quotient and remainder is zero. (Note – if remainder will not zero, means doesn’t divide exactly, try next prime number to divide)
Step 2: Again we divide the quotient 50 by smallest prime number i.e. 2. We got 25 as quotient.
Step 3: Again we divide 25 by smallest prime number, i.e. 2. But 2 doesn’t divide 25 completely. So we have try to divide by next prime numbers i.e. 3 or 5. (Repeat step 2 and 3 until we got 1 as a quotient.)
Hence, 100 = 2 x 2 x 5 x 5 = 22 x 52
So 100 has two prime factor i.e. 2 & 5.
Method #2 (Factor Tree Method)
Step 1 : Write a number as 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 root)
Step 3 : Repeat step 2 until we can’t factor any more (or until we got prime factor)
Step 4 : The end nodes are the prime factors.
Factor Tree of 55
In First Tree ( see above figure), We can initiate the tree by choosing any two factors. Here we choose 5 and 11 as factors of 55.
Since, 5 and 11 are prime numbers and no further split can be made. Hence, 55 has only two prime factors i.e. 5 and 11.
In second example of 100 :
We choose 2 and 50 as initial nodes in first fig. ( We can choose any factors as initial factors as in other figures)
Further, we have to divide these nodes. Since 2 is a prime number, so it can’t be split further. But 50 can be split in 2 and 25.
Repeat this process till we got prime nodes.
Here, in each factor tree of 100 we got same node that are 2, 2, 5, 5 .
Hence, we can say that 100 has only two prime factors i.e. 2 and 5.
Note:- The Factor Tree may be made so many types depends upon choosing the initial and middle factors.
Number of factors of 55
To find the number of factors, we use Method #1 (Division Method).
In our example, as we saw above 55 = 5 x 11 means 5 to the power 1 multiply 11 to the power 1
Number of factors is = (power + 1)(power + 1)(power + 1)………. = (1 + 1)(1 + 1) = 2 x 2 = 4
if we consider both positive and negative factors, then
total no. of factors = 4 (positive) + 4 (negative) = 8
Take another example, 100 = 2 x 2 x 5 x 5 = 22 x 52
Number of factors of 100 is = (2 + 1)(2 + 1) = 3 x 3 =9
and if we consider both positive and negative factors, then
total no. of factors = 9 (positive) + 9 (negative) = 18
I hope, this step-by-step tutorial will be helpful to understand factorization method of 55.
Try another number 56 for factors.
Take a another look of factorization on Quora.