Factors of 638

The numbers that divide 638 evenly are known as factors of 638. A factor of 638 is a number that divides the number without remainder. The factors of 638 are 1, 2, 7, 14, 29, 58, 91, 182, 319, and 638.

Negative factors of 638: -1, -2, -7, -14, -29, -58, -91, -182, -319, and -638.

Prime factors of 638: 2, 7, and 29.

Prime factorization of 638: 2 × 7 × 29.

The sum of factors of 638: 1 + 2 + 7 + 14 + 29 + 58 + 91 + 182 + 319 + 638 = 1341

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 638. Identifying the numbers which are multiplied to get the number 638 is the multiplication method.

Step 1: Multiply 638 by 1, 638 × 1 = 638.

Step 2: Check for other numbers that give 638 after multiplying

2 × 319 = 638

7 × 91 = 638

14 × 45.571 (not a factor as 45.571 is not a whole number)

29 × 22 = 638

Therefore, the positive factor pairs of 638 are: (1, 638), (2, 319), (7, 91), and (29, 22). All these factor pairs result in 638. 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 638 by 1, 638 ÷ 1 = 638.

Step 2: Continue dividing 638 by the numbers until the remainder becomes 0.

638 ÷ 1 = 638

638 ÷ 2 = 319

638 ÷ 7 = 91

638 ÷ 29 = 22

Therefore, the factors of 638 are: 1, 2, 7, 14, 29, 58, 91, 182, 319, and 638.

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

638 ÷ 2 = 319

319 ÷ 7 = 45.571 (not a factor as the result is not a whole number)

319 ÷ 29 = 11

11 ÷ 11 = 1

The prime factors of 638 are 2, 7, and 29.

The prime factorization of 638 is: 2 × 7 × 29.

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

Step 1: Firstly, 638 is divided by 2 to get 319.

Step 2: Now divide 319 by 7 (not a factor as the result is not a whole number)

Step 3: Divide 319 by 29 to get 11.

Step 4: Divide 11 by 11. Here, 11 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 638 is: 2 × 7 × 29.

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 638: (1, 638), (2, 319), (7, 91), (14, 45.571), and (29, 22).
• Negative factor pairs of 638: (-1, -638), (-2, -319), (-7, -91), (-14, -45.571), and (-29, -22).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 638 are 1, 2, 7, 14, 29, 58, 91, 182, 319, and 638.

• Prime factors: The factors which are prime numbers. For example, 2, 7, and 29 are prime factors of 638.

• 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 638 are (1, 638), (2, 319), etc.

• Prime factorization: A way of expressing a number as a product of its prime factors. For example, the prime factorization of 638 is 2 × 7 × 29.

• Multiple: A number that can be divided by another number without leaving a remainder. For example, 638 is a multiple of 2, 7, and 29.