Factors of 648

The numbers that divide 648 evenly are known as factors of 648. A factor of 648 is a number that divides the number without remainder. The factors of 648 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, and 648.

Negative factors of 648: -1, -2, -3, -4, -6, -8, -9, -12, -18, -24, -27, -36, -54, -72, -81, -108, -162, -216, -324, and -648.

Prime factors of 648: 2 and 3.

Prime factorization of 648: 2^{3 x} 3⁴.

The sum of factors of 648: 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 24 + 27 + 36 + 54 + 72 + 81 + 108 + 162 + 216 + 324 + 648 = 2016

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 648. Identifying the numbers which are multiplied to get the number 648 is the multiplication method.

Step 1: Multiply 648 by 1, 648 × 1 = 648.

Step 2: Check for other numbers that give 648 after multiplying

2 × 324 = 648

3 × 216 = 648

4 × 162 = 648

6 × 108 = 648

8 × 81 = 648

9 × 72 = 648

12 × 54 = 648

18 × 36 = 648

24 × 27 = 648

Therefore, the positive factor pairs of 648 are: (1, 648), (2, 324), (3, 216), (4, 162), (6, 108), (8, 81), (9, 72), (12, 54), (18, 36), (24, 27). For every positive factor, there is a negative factor.

Dividing the given numbers with 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 648 by 1, 648 ÷ 1 = 648.

Step 2: Continue dividing 648 by the numbers until the remainder becomes 0.

648 ÷ 1 = 648

648 ÷ 2 = 324

648 ÷ 3 = 216

648 ÷ 4 = 162

648 ÷ 6 = 108

648 ÷ 8 = 81

648 ÷ 9 = 72

648 ÷ 12 = 54

648 ÷ 18 = 36

648 ÷ 24 = 27

Therefore, the factors of 648 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648.

The factors can be found by dividing it with prime numbers. 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 648 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

648 ÷ 2 = 324

324 ÷ 2 = 162

162 ÷ 2 = 81

81 ÷ 3 = 27

27 ÷ 3 = 9

9 ÷ 3 = 3

3 ÷ 3 = 1

The prime factors of 648 are 2 and 3. The prime factorization of 648 is: 2^{3 x} 3⁴

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

Step 1: Firstly, 648 is divided by 2 to get 324.

Step 2: Now divide 324 by 2 to get 162.

Step 3: Then divide 162 by 2 to get 81.

Step 4: Divide 81 by 3 to get 27.

Step 5: Divide 27 by 3 to get 9.

Step 6: Divide 9 by 3 to get 3. Here, 3 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 648 is: 2³ x 3⁴.

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 648: (1, 648), (2, 324), (3, 216), (4, 162), (6, 108), (8, 81), (9, 72), (12, 54), (18, 36), (24, 27).
• Negative factor pairs of 648: (-1, -648), (-2, -324), (-3, -216), (-4, -162), (-6, -108), (-8, -81), (-9, -72), (-12, -54), (-18, -36), (-24, -27).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 648 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, and 648.

• Prime factors: The factors which are prime numbers. For example, 2 and 3 are prime factors of 648.

• Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 648 is (2³ x3⁴).

• 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 648 are (1, 648), (2, 324), etc.

• Multiple: A multiple is a product of a number and another integer. For example, 648 is a multiple of 9.