Education

How to Factor Numbers?


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Factoring Calculator: If you ever need assistance with finding factors of a given number take the help of the online tool provided. Just enter the input integer and you will get the factors in the blink of an eye. Scroll down to find the detailed procedure on how to evaluate Factoring using different methods. To help you out, we even jotted down the solved examples showing step by step.

How to Factor Numbers?

Use the simple procedure on how to factor numbers using the trial division method. Following it you will arrive at the solution easily. They are along the lines

  • Find the square root of an integer number n and round it to the closest number. Let the number be s
  • Start with 1 and find the corresponding factor pair n ÷ 1 = n. Thus 1, n are factor pairs as the division results in a whole number leaving a remainder zero.
  • Continue the process with number 2 and test all the integers (n ÷ 2, n ÷ 3, n ÷ 4… n ÷ s) through the square root rounded to s. List out the factor pairs wherein the remainder is zero.
  • By the time you have reached n ÷ s and noted all the factor pairs, you are done with the successful factoring of n.

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Example

What are the Factors of 14

Solution: 

The Square root of 14 is 3.7416 and rounding it we get 4

Testing the integer value 1 through 4 for the division into 14 and checking for the factors that leave a remainder zero.

The numbers that leave a remainder zero when dividing the number 14 are 1, 2, 7, 14

Factor Pairs are (1,14)(2,7)(7,2)(14,1)

Take the help of Factoring Calculator to evaluate the Factors of Number 25 i.e. 1, 5, 25 the integers that divide the number 25 leaving a remainder zero.

Factor Tree of 25 to evaluate the factors

  • Split the number 25 into two factors that can result in the same product after multiplication. That means 5*5 = 25
  • 5 is a Prime number and the procedure ends here as the numbers can’t be expressed as a product anymore. Factor Tree of 25 looks as under

Here are some samples of factoring calculations.

How to find Factors of 25?

To find factors of 25 check for the numbers that divide 25 exactly and leaves a remainder zero. Check for all the integers that divide 25 by all the numbers up to 25. Make a note of numbers that results in the remainder zero.

1, 5, 25 are factors that divide 25 leaving a remainder zero.

Factoring Calculator | Table of Factors from 1 to 100

NumberFactorsPrime or Composite
11Neither prime nor composite
21, 2Prime
31, 3Prime
41, 2, 4Composite
51, 5Prime
61, 2, 3, 6Composite
71, 7Prime
81, 2, 4, 8Composite
91, 3, 9Composite
101, 2, 5, 10Composite
111, 11Prime
121, 2, 3, 4, 6, 12Composite
131, 13Prime
141, 2, 7, 14Composite
151, 3, 5, 15Composite
161, 2, 4, 8, 16Composite
171, 17Prime
181, 2, 3, 6, 9, 18Composite
191, 19Prime
201, 2, 4, 5, 10, 20Composite
211, 3, 7, 21Composite
221, 2, 11, 22Composite
231, 23Prime
241, 2, 3, 4, 6, 8, 12, 24Composite
251, 5, 25Composite
261, 2, 13, 26Composite
271, 3, 9, 27Composite
281, 2, 4, 7, 14, 28Composite
291, 29Prime
301, 2, 3, 5, 6, 10, 15, 30Composite
311, 31Prime
321, 2, 4, 8, 16, 32Composite
331, 3, 11, 33Composite
341, 2, 17, 34Composite
351, 5, 7, 35Composite
361, 2, 3, 4, 6, 9, 12, 18, 36Composite
371, 37Prime
381, 2, 19, 38Composite
391, 3, 13, 39Composite
401, 2, 4, 5, 8, 10, 20, 40Composite
411, 41Prime
421, 2, 3, 6, 7, 14, 21, 42Composite
431, 43Prime
441, 2, 4, 11, 22, 44Composite
451, 3, 5, 9, 15, 45Composite
461, 2, 23, 46Composite
471, 47Prime
481, 2, 3, 4, 6, 8, 12, 16, 24, 48Composite
491, 7, 49Composite
501, 2, 5, 10, 25, 50Composite
511, 3, 17, 51Composite
521, 2, 4, 13, 26, 52Composite
531, 53Prime
541, 2, 3, 6, 9, 18, 27, 54Composite
551, 5, 11, 55Composite
561, 2, 4, 7, 8, 14, 28, 56Composite
571, 3, 19, 57Composite
581, 2, 29, 58Composite
591, 59Prime
601, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60Composite
611, 61Prime
621, 2, 31, 62Composite
631, 3, 7, 9, 21, 63Composite
641, 2, 4, 8, 16, 32, 64Composite
651, 5, 13, 65Composite
661, 2, 3, 6, 11, 22, 33, 66Composite
671, 67Prime
681, 2, 4, 17, 34, 68Composite
691, 3, 23, 69Composite
701, 2, 5, 7, 10, 14, 35, 70Composite
711, 71Prime
721, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72Composite
731, 73Prime
741, 2, 37, 74Composite
751, 3, 5, 15, 25, 75Composite
761, 2, 4, 19, 38, 76Composite
771, 7, 11, 77Composite
781, 2, 3, 6, 13, 26, 39, 78Composite
791, 79Prime
801, 2, 4, 5, 8, 10, 16, 20, 40, 80Composite
811, 3, 9, 27, 81Composite
821, 2, 41, 82Composite
831, 83Prime
841, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84Composite
851, 5, 17, 85Composite
861, 2, 43, 86Composite
871, 3, 29, 87Composite
881, 2, 4, 8, 11, 22, 44, 88Composite
891, 89Prime
901, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90Composite
911, 7, 13, 91Composite
921, 2, 4, 23, 46, 92Composite
931, 3, 31, 93Composite
941, 2, 47, 94Composite
951, 5, 19, 95Composite
961, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96Composite
971, 97Prime
981, 2, 7, 14, 49, 98Composite
991, 3, 9, 11, 33, 99Composite
1001, 2, 4, 5, 10, 20, 25, 50, 100Composite

Example: All the factors of 12

  • 2 × 6 = 12,
  • but also 3 × 4 = 12,
  • and of course 1 × 12 = 12.

So 1, 2, 3, 4, 6 and 12 are factors of 12.

And also -1,-2,-3,-4,-6 and -12, because you get a positive number when you multiply two negatives, such as (-2)×(-6) = 12

Answer: 1, 2, 3, 4, 6, 12, -1, -2, -3, -4, -6, -12

Factoring Calculator – How Can I Do It Myself?

Work from the outside in!

Example: All the factors of 20.

Start at 1: 1×20=20, so put 1 at the start, and put its “partner” 20 at the other end:

120

Then try 2. 2×10=20 works, so put in 2 and 10:

121020

Then try 3. 3 doesn’t work (3×6=18 is too low, 3×7=21 is too high).

Then try 4. 4×5=20 works, so put them in:

12451020

There is no whole number between 4 and 5 so you are done! (Don’t forget the negative ones).

12451020
-1-2-4-5-10-20

FAQs on Factoring Numbers | Factors of a Number Calculator

1. What is a factor?

A factor is a number that divides into another number exactly and without leaving a remainder.

2. How to find factoring of numbers easily?

Take the help of the Factoring Calculator to find factors of given numbers in the blink of an eye.

3. Where do I get a detailed procedure on Factoring Numbers?

You can get a detailed procedure on factoring numbers on our page.

4. Where can I find Solved Examples on Factoring?

You can find Solved Examples on Factoring provided with detailed steps on our page.

5.  What are the Factors of 25?

Factors of 25 are 1, 5, 25.

6. How to find Factors of 25?

You can find Factors of 25 by simply dividing with all the integers up to 25. Factors are those numbers that leave a remainder zero.

7. Where do I get the detailed procedures on finding factors of 25?

You can get a detailed procedure on finding factors of 25 on our page.

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