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Factor Calculator

Factors are the whole numbers that divide a number exactly. Test every number from 1 up to its square root; each one that divides gives a pair. For 36: 1 × 36, 2 × 18, 3 × 12, 4 × 9 and 6 × 6, so its 9 factors are 1, 2, 3, 4, 6, 9, 12, 18 and 36, and 36 = 2² × 3².

Inputs

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Inputs
Factor pairs of 36Factor pairs of 361 × 361 wide × 36 long2 × 182 wide × 18 long3 × 123 wide × 12 long4 × 94 wide × 9 long6 × 66 wide × 6 longmyconstructioncalculator.com
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Results

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Factors of 36
1, 2, 3, 4, 6, 9, 12, 18, 36
Number of factors9
Factor pairs1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6
Prime factors2² × 3²
Sum of the factors91
Prime?No
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Working
  1. Try every whole number from 1 up to √36 = 6.00. Each one that divides exactly gives a pair: 36 ÷ 1 = 36; 36 ÷ 2 = 18; 36 ÷ 3 = 12; 36 ÷ 4 = 9; 36 ÷ 6 = 6
  2. Both numbers of every pair are factors: 9 in all.
  3. Prime factors: 36 = 2² × 3²
Results are estimates for planning and material ordering only. They are not a substitute for structural design or approval by a qualified engineer. Read the full disclaimer.
Formula


Test d = 1, 2, 3, … up to √n
If n ÷ d is whole, then d and n ÷ d are both factors
Prime factors: divide by the smallest prime again and again


Worked Example


Factors of 36:


    

  1. √36 = 6, so test 1 to 6
    2. 

  2. 36 ÷ 1 = 36, 36 ÷ 2 = 18, 36 ÷ 3 = 12, 36 ÷ 4 = 9, 36 ÷ 6 = 6 (5 does not divide)
    3. 

  3. Factors: 1, 2, 3, 4, 6, 9, 12, 18, 36 (9 factors)
    4. 



Factors of Common Numbers






Number
Prime factors
Number of factors






12
2² × 3
6




24
2³ × 3
8




36
2² × 3²
9




48
2⁴ × 3
10




60
2² × 3 × 5
12




72
2³ × 3²
12




100
2² × 5²
9




120
2³ × 3 × 5
16




360
2³ × 3² × 5
24






Frequently Asked Questions
How do you find all the factors of a number?
Divide by 1, 2, 3 and so on up to the square root. Every exact division gives two factors: the divisor and the answer. For 24: 1 × 24, 2 × 12, 3 × 8 and 4 × 6, so 8 factors.
What is a factor pair?
Two numbers that multiply to give the number. The factor pairs of 36 are 1 × 36, 2 × 18, 3 × 12, 4 × 9 and 6 × 6.
Why do square numbers have an odd number of factors?
One of their pairs is a number times itself, such as 6 × 6 for 36, and it counts once. Every other number has its factors in pairs, so an even count.
What is prime factorisation?
Writing a number as a product of primes only. 360 = 2³ × 3² × 5. Every whole number above 1 has exactly one prime factorisation.
How are factors used on site?
To split a length or quantity into equal whole parts. A 3.6 m run divides into equal bays of any factor of 360 cm: 120, 90, 72, 60, 45 or 40 cm, for example.
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