Factors of 24

Factors of 24 are the list of integers that can be evenly divided into 24. There are overall 8 factors of 24 among which 24 is the biggest factor and 1, 2, 3, 4, 6, 8, 12, and 24 are positive factors. The sum of all factors of 24 is 60 and its factors in Pairs are (1, 24), (2, 12), (3, 8), and (4, 6).

• Factors of 24: 1, 2, 3, 4, 6, 8, 12 and 24
• Negative Factors of 24: -1, -2, -3, -4, -6, -8, -12 and -24
• Prime Factors of 24: 2, 3
• Prime Factorization of 24: 2 × 2 × 2 × 3 = 2³ × 3
• Sum of Factors of 24: 60

Before we move ahead, let's recall a little about factors. A factor is a number that divides the given number without any remainder. Factors of 24 are pairs of those numbers whose product results in 24.

Important Notes:

• Factors of a number may be prime numbers or composite numbers.
• Factors are always whole numbers. They are never fractions or decimals.

To calculate the factors of any number, here in this case 24, we need to find all the numbers that would divide 24 without leaving any remainder. We start with the number 1, then check for numbers 2, 3, 4, 5, 6, 7, etc. up to 24 respectively. The number 1 and the number itself would always be a factor of the given number.

Let us check the division of 24 by its factors. We express 24 as a product of its prime factors in the prime factorization method and we divide 24 with its divisors in the division method. Let us see which numbers divide 24 exactly without a remainder in which case the divisors, as well as the quotients, are the factors of 24.

• 24/1 = 24; therefore, 1 and 24 are factors of 24
• 24/2 = 12; therefore, 2 is a factor of 24
• 24/3 = 8; therefore, 3 is a factor of 24
• 24/4 = 6; therefore, 4 is a factor of 24

Hence, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. To understand the concept of finding factors by prime factorization better, let us take a few more examples.

• Factors of 224 - The factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224
• Factors of 243 - The factors of 243 are 1, 3, 9, 27, 81, 243
• Factors of 245 - The factors of 245 are 1, 5, 7, 35, 49, 245
• Factors of 21 - The factors of 21 are 1, 3, 7, 21
• Factors of 42 - The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
• Factors of 48 - The factors of 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Prime factorization means expressing a composite number as the product of its prime factors. Factors of 24 by prime factorization are given by using the following steps:

Step 1: Write the pair of factors, which on multiplication, gives the required number.

• 24 can be factored as a product of 4 and 6.

Step 2: Check each of the factors to see whether each one of them is prime or not.

• 4 is not a prime number and can be dissociated as a product of 2 by itself or as a square of 2.
• 6 is not a prime number and can be dissociated as a product of 2 and 3.

Step 3: As per the criteria,

• 24 can be written as 24 = 4 × 6 = 2 × 2 × 2 × 3
• It can also be written as 24 = 2³ × 3

Pair factors are pairs of those numbers that, when multiplied, give the product as the required number. Here, the required number is 24. Let's try visualizing it using blocks.

Factors of 24 in pairs can be written as:

These factors given above are positive pair factors. It is possible to have negative pair factors as well because the product of two negative numbers also gives a positive number.

Let's have a look at negative pair factors.

• 1 is the smallest factor of every number.
• Every number has a minimum of two factors, i.e. 1 and the number itself.
• All even numbers always have 2 as one of their factors.
• All the numbers which end in 5, will always have 5 as one of their factors.
• All the numbers which end in 0, will always have 1, 2, 5, and 10 as their factors.

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