Factors of 624

The numbers that divide 624 evenly are known as factors of 624. A factor of 624 is a number that divides the number without remainder. The factors of 624 are 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 208, 312, and 624.

Negative factors of 624: -1, -2, -3, -4, -6, -8, -12, -13, -16, -24, -26, -39, -48, -52, -78, -104, -156, -208, -312, and -624.

Prime factors of 624: 2 and 3, 13.

Prime factorization of 624: (2⁴ × 3 × 13).

The sum of factors of 624: 1 + 2 + 3 + 4 + 6 + 8 + 12 + 13 + 16 + 24 + 26 + 39 + 48 + 52 + 78 + 104 + 156 + 208 + 312 + 624 = 1680

Factors can be found using different methods. Mentioned below are some commonly used methods:

1. Finding factors using multiplication
2. Finding factors using division method
3. Prime factors and Prime factorization

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 624. Identifying the numbers which are multiplied to get the number 624 is the multiplication method.

Step 1: Multiply 624 by 1, (624 × 1 = 624).

Step 2: Check for other numbers that give 624 after multiplying 2 × 312 = 624

3 × 208 = 624

4 × 156 = 624

6 × 104 = 624

8 × 78 = 624

12 × 52 = 624

13 × 48 = 624

16 × 39 = 624

24 × 26 = 624

Therefore, the positive factor pairs of 624 are: (1, 624), (2, 312), (3, 208), (4, 156), (6, 104), (8, 78), (12, 52), (13, 48), (16, 39), (24, 26). For every positive factor, there is a negative factor.

Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method -

Step 1: Divide 624 by 1, \(624 ÷ 1 = 624\).

Step 2: Continue dividing 624 by the numbers until the remainder becomes 0.

624 ÷ 1 = 624

624 ÷ 2 = 312

624 ÷ 3 = 208

624 ÷ 4 = 156

624 ÷ 6 = 104

624 ÷ 8 = 78

624 ÷ 12 = 52

624 ÷ 13 = 48

624 ÷ 16 = 39\

624 ÷ 24 = 26

Therefore, the factors of 624 are: 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 208, 312, and 624.

The factors can be found by dividing it with a prime number. We can find the prime factors using the following methods:

• Using prime factorization
• Using factor tree

Using Prime Factorization: In this process, prime factors of 624 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

624 ÷ 2 = 312

312 ÷ 2 = 156

156 ÷ 2 = 78

78 ÷ 2 = 39

39 ÷ 3 = 13

13 ÷ 13 = 1

The prime factors of 624 are 2, 3, and 13. The prime factorization of 624 is: (2⁴ × 3 × 13).

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -

Step 1: Firstly, 624 is divided by 2 to get 312.

Step 2: Now divide 312 by 2 to get 156.

Step 3: Then divide 156 by 2 to get 78.

Step 4: Divide 78 by 2 to get 39.

Step 5: Divide 39 by 3 to get 13.Here, 13 is the smallest prime number, that cannot be divided anymore.

So, the prime factorization of 624 is: (2⁴ × 3 × 13).

Factor Pairs: Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.

• Positive factor pairs of 624: (1, 624), (2, 312), (3, 208), (4, 156), (6, 104), (8, 78), (12, 52), (13, 48), (16, 39), and (24, 26).
• Negative factor pairs of 624: (-1, -624), (-2, -312), (-3, -208), (-4, -156), (-6, -104), (-8, -78), (-12, -52), (-13, -48), (-16, -39), and (-24, -26).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 624 are 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 208, 312, and 624.

• Prime factors: The factors which are prime numbers. For example, 2, 3, and 13 are prime factors of 624.

• Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 624 are (1, 624), (2, 312), etc.

• Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 624 is (2⁴ × 3 × 13).

• Multiple: A number that can be divided by another number without a remainder. For example, 624 is a multiple of 12.