Factors of 657

The numbers that divide 657 evenly are known as factors of 657. A factor of 657 is a number that divides the number without remainder. The factors of 657 are 1, 3, 9, 73, 219, and 657.

Negative factors of 657: -1, -3, -9, -73, -219, and -657.

Prime factors of 657: 3 and 73.

Prime factorization of 657: 3² × 73.

The sum of factors of 657: 1 + 3 + 9 + 73 + 219 + 657 = 962

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 657. Identifying the numbers that are multiplied to get the number 657 is the multiplication method.

Step 1: Multiply 657 by 1, 657 × 1 = 657.

Step 2: Check for other numbers that give 657 after multiplying 3 × 219 = 657 9 × 73 = 657

Therefore, the positive factor pairs of 657 are: (1, 657), (3, 219), (9, 73). All these factor pairs result in 657. 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 657 by 1, 657 ÷ 1 = 657.

Step 2: Continue dividing 657 by the numbers until the remainder becomes 0.

657 ÷ 1 = 657

657 ÷ 3 = 219

657 ÷ 9 = 73

Therefore, the factors of 657 are: 1, 3, 9, 73, 219, 657.

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

657 ÷ 3 = 219

219 ÷ 3 = 73

73 ÷ 73 = 1

The prime factors of 657 are 3 and 73. The prime factorization of 657 is: 3² × 73.

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

Step 1: Firstly, 657 is divided by 3 to get 219.

Step 2: Now divide 219 by 3 to get 73.

Step 3: 73 is a prime number and cannot be divided further. So, the prime factorization of 657 is: 3² × 73.

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 657: (1, 657), (3, 219), and (9, 73).
• Negative factor pairs of 657: (-1, -657), (-3, -219), and (-9, -73).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 657 are 1, 3, 9, 73, 219, and 657.

• Prime factors: The factors which are prime numbers. For example, 3 and 73 are prime factors of 657.

• 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 657 are (1, 657), (3, 219), and (9, 73).

• Prime Factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 657 is 3² × 73.

• Negative Factors: Factors of a number that are negative, such as -1, -3, -9, -73, -219, -657 for the number 657.