Factors of 24 are basically the numbers that divide it evenly or exactly without leaving any remainder i.e if a number divides 24 with a remainder of zero, then that number is called a factor.
- All Factors: 1, 2, 3, 4, 6, 8, 12 and 24.
- Prime factors: 2, 3.
- Factors in pairs: (1,24), (2,12), (3,8), (4,6),(6,4),(8,3),(12,2).
Index
Prime factorization of 24
Prime factorization is a method of “expressing” or finding the given number as the product of prime numbers. If a number occurs more than once in prime factorization, it is usually expressed in exponential form to make it more compact.
The prime factorization comes out to be: 2 × 2 × 2 × 3 = 23 × 3.
Prime factorization of 24 by Upside-Down Division Method
Upside-Down Division is one of the techniques used to do the Prime factorization of different numbers.
In this method, you will divide a given “composite” number evenly by the several prime numbers(starting from the smallest) till it gets a prime number.
It is called Upside-Down Division because the symbol is flipped upside down.
Here, 24 is an even number. So it is undoubtedly divisible by 2 with no remainder. Thus, 2 is its smallest prime factor.
And we get 24÷ 2 = 12. Now find the prime factors of the obtained quotient.
Repeat Step 1 and Step 2 until we get a result of prime number as the quotient. Here, 12is the quotient.
12÷ 2 = 6. Here, 6 is the quotient. Now find the prime factors of the 6.
6÷ 2= 3. Here, 3 is the prime number.
So we can stop the process.
So, prime factorization with upside-down division method comes out to be: 2 × 2 × 2 × 3 = \(2^3 \times 3\).
Prime factorization of 24 by Factor Tree Method
The Factor tree method is another technique for producing the prime factorization and all factors of a given number.
To use this method for a number x,
Firstly consider two factors say a,b of x such that a*b is equal to x and at least one of them (a, b) is a prime factor say a.
Then consider two factors of b say c, d such that again at least one of them is a prime factor. This process is repeated until both the factors are prime i.e if we get both the factors as prime at any step, we stop the process there.
Following is the factor tree of the given number.
Here we can get the prime factorisation of 24 as 2 * 2 * 2 * 3 and the two prime factors are 2, 3
FAQs
Sum of all factors of the required number = (23 + 1 – 1)/(2 – 1) × (31 + 1 – 1)/(3 – 1) = 60
Since, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24 and the factors of 21 are 1, 3, 7, 21.
Hence, [1, 3] are the common factors of 24 and 21.
The prime factors of the number are 2, 3.
More factors:
