Factors of 637

The numbers that divide 637 evenly are known as factors of 637. A factor of 637 is a number that divides the number without remainder. The factors of 637 are 1, 7, 91, and 637.

Negative factors of 637: -1, -7, -91, and -637.

Prime factors of 637: 7 and 91.

Prime factorization of 637: 7 × 91.

The sum of factors of 637: 1 + 7 + 91 + 637 = 736

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

1. Finding factors using multiplication
2. Finding factors using the 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 637. Identifying the numbers which are multiplied to get the number 637 is the multiplication method.

Step 1: Multiply 637 by 1, 637 × 1 = 637.

Step 2: Check for other numbers that give 637 after multiplying 7 × 91 = 637

Therefore, the positive factor pairs of 637 are: (1, 637) and (7, 91).

All these factor pairs result in 637. 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 637 by 1, 637 ÷ 1 = 637.

Step 2: Continue dividing 637 by the numbers until the remainder becomes 0.

637 ÷ 1 = 637

637 ÷ 7 = 91

637 ÷ 91 = 7

Therefore, the factors of 637 are: 1, 7, 91, 637.

The factors can be found by dividing them 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 637 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

637 ÷ 7 = 91

91 ÷ 7 = 13

13 ÷ 13 = 1

The prime factors of 637 are 7 and 13.

The prime factorization of 637 is: 7 × 13.

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

Step 1: Firstly, 637 is divided by 7 to get 91.

Step 2: Now divide 91 by 7 to get 13.

Step 3: Here, 13 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 637 is: 7 × 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 637: (1, 637) and (7, 91).
• Negative factor pairs of 637: (-1, -637) and (-7, -91).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 637 are 1, 7, 91, and 637.

• Prime factors: The factors which are prime numbers. For example, 7 and 13 are prime factors of 637.

• 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 637 are (1, 637) and (7, 91).

• Multiplication method: A method to find factors by identifying pairs of numbers multiplied to give the original number.

• Division method: A method to find factors by dividing the number with whole numbers until the remainder is zero.