Factors of 644

The numbers that divide 644 evenly are known as factors of 644. A factor of 644 is a number that divides the number without remainder. The factors of 644 are 1, 2, 4, 7, 14, 23, 28, 46, 92, 161, 322, and 644.

Negative factors of 644: -1, -2, -4, -7, -14, -23, -28, -46, -92, -161, -322, and -644.

Prime factors of 644: 2, 7, and 23.

Prime factorization of 644: 2² × 7 × 23.

The sum of factors of 644: 1 + 2 + 4 + 7 + 14 + 23 + 28 + 46 + 92 + 161 + 322 + 644 = 1344

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 644. Identifying the numbers which are multiplied to get the number 644 is the multiplication method.

Step 1: Multiply 644 by 1, 644 × 1 = 644.

Step 2: Check for other numbers that give 644 after multiplying

2 × 322 = 644

4 × 161 = 644

7 × 92 = 644

14 × 46 = 644

23 × 28 = 644

Therefore, the positive factor pairs of 644 are: (1, 644), (2, 322), (4, 161), (7, 92), (14, 46), (23, 28). All these factor pairs result in 644. 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 644 by 1, 644 ÷ 1 = 644.

Step 2: Continue dividing 644 by the numbers until the remainder becomes 0.

644 ÷ 1 = 644

644 ÷ 2 = 322

644 ÷ 4 = 161

644 ÷ 7 = 92

644 ÷ 14 = 46

644 ÷ 23 = 28

Therefore, the factors of 644 are: 1, 2, 4, 7, 14, 23, 28, 46, 92, 161, 322, 644.

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 644 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

644 ÷ 2 = 322

322 ÷ 2 = 161

161 ÷ 7 = 23

23 ÷ 23 = 1

The prime factors of 644 are 2, 7, and 23. The prime factorization of 644 is: 2² × 7 × 23.

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

Step 1: Firstly, 644 is divided by 2 to get 322.

Step 2: Now divide 322 by 2 to get 161.

Step 3: Then divide 161 by 7 to get 23. Here, 23 is the smallest prime number, which cannot be divided anymore. So, the prime factorization of 644 is: 2² × 7 × 23.

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 644: (1, 644), (2, 322), (4, 161), (7, 92), (14, 46), (23, 28).
• Negative factor pairs of 644: (-1, -644), (-2, -322), (-4, -161), (-7, -92), (-14, -46), (-23, -28).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 644 are 1, 2, 4, 7, 14, 23, 28, 46, 92, 161, 322, and 644.

• Prime factors: The factors which are prime numbers. For example, 2, 7, and 23 are prime factors of 644.

• 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 644 are (1, 644), (2, 322), etc.

• Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 644 is 2² × 7 × 23.

• Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number. For example, 23 × 28 = 644 is one factor pair.