Factors of 30 are the numbers, which gives the result as 30 when multiplied together in pair of two. We can also say factors are the numbers which divide a number completely, leaving zero as remainder. All the composite numbers such as 24, 36, 42, etc. have their factor numbers. To find the factors of a number, 30, we will use the multiplication method here. The multiples of 30 are easy to evaluate and they areÂ 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, 360, 390, 420 and so on.
What are factors of 30?
The factors of 30 are the numbers which can divide the number 30 completely. These factors are nothing but the real numbers or positive integers. Although the negative factors also result in original number such as: (-2) x (-15) = 30. But in Maths, we only consider positive factors. Hence the factors of real number 30 are 1,2,3,5,6,10, 15 and 30.
If we notice here, each factor acts as the divisor of 30, which means:
- 30 Ã· 1 = 30
- 30 Ã· 2 = 15
- 30 Ã· 3 = 10
- 30 Ã· 5 = 6
- 30 Ã· 6 = 5
- 30 Ã· 10 = 3
- 30 Ã· 15 = 2
- 30 Ã· 30 = 1
Hence, you can see, in the above operation performed, there are no remainders left. Each real number other than 0 and 1 have their factors.
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Common Factors of 30
The factors of number 30 as we discussed areÂ 1,2,3,5,6,10, 15 and 30. Common factors are the numbers which are common for two or more numbers.Â Suppose the common factors of 15 and 30 are 1, 3, 5 and 15, since the factors of 15 are 1, 3, 5 and 15 which are also common for number 30.
Factors Of 30 in Pairs
We can find the pair factors of number 30, by multiplying two numbers in a pair to get the original number as 30, such as;
- 1 Ã— 30 = 30
- 2 Ã— 15 = 30
- 3 Ã— 10 = 30
- 5 Ã— 6 = 30
Therefore, factors in pairs which on multiplication gives the original number 30 are (1,30), (2,15), (3,10) and (5,6).
Prime Factorisation of 30
The number 30 is a composite number. Now let us find the prime factors of it.
- The first step is to divide the number 30 with the smallest prime factor,i.e. 2.
30 Ã· 2 = 15
Â Â Â Â Â Again, divide 15 by 2.
15 Ã· 2 = 7.5; factor cannot be a fraction.
- Now, proceed to the next prime numbers, i.e. 3 and divide 15 with it.
15 Ã· 3 = 5
Â Â Â Â Â Again, if we divide 5 by 3, we get a fraction number, which we cannot consider as a factor.Â Â Â Â Â Â Â Â Â Â Â Â Â Â Therefore, we will move to the next prime number, which is 5.
5 Ã· 5 = 1
- We have received 1 at the end and further, we cannot proceed with the division method, as 1 donâ€™t have any multiples. So, the prime factors of 30 are 2 Ã— 3 Ã— 5, where 2, 3 and 5 are the prime numbers.
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