Factors of 654

The numbers that divide 654 evenly are known as factors of 654. A factor of 654 is a number that divides the number without remainder. The factors of 654 are 1, 2, 3, 6, 109, 218, 327, and 654.

Negative factors of 654: -1, -2, -3, -6, -109, -218, -327, and -654.

Prime factors of 654: 2, 3, and 109.

Prime factorization of 654: 2 × 3 × 109.

The sum of factors of 654: 1 + 2 + 3 + 6 + 109 + 218 + 327 + 654 = 1320

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 654. Identifying the numbers which are multiplied to get the number 654 is the multiplication method.

Step 1: Multiply 654 by 1, 654 × 1 = 654.

Step 2: Check for other numbers that give 654 after multiplying

2 × 327 = 654

3 × 218 = 654

6 × 109 = 654

Therefore, the positive factor pairs of 654 are: (1, 654), (2, 327), (3, 218), (6, 109). All these factor pairs result in 654. 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 results as whole numbers as factors. Factors can be calculated by following a simple division method -

Step 1: Divide 654 by 1, 654 ÷ 1 = 654.

Step 2: Continue dividing 654 by the numbers until the remainder becomes 0.

654 ÷ 1 = 654

654 ÷ 2 = 327

654 ÷ 3 = 218

654 ÷ 6 = 109

Therefore, the factors of 654 are: 1, 2, 3, 6, 109, 218, 327, 654.

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

654 ÷ 2 = 327

327 ÷ 3 = 109

109 ÷ 109 = 1

The prime factors of 654 are 2, 3, and 109. The prime factorization of 654 is: 2 × 3 × 109.

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

Step 1: Firstly, 654 is divided by 2 to get 327.

Step 2: Now divide 327 by 3 to get 109.

Step 3: Here, 109 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 654 is: 2 × 3 × 109.

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 654: (1, 654), (2, 327), (3, 218), and (6, 109).
• Negative factor pairs of 654: (-1, -654), (-2, -327), (-3, -218), and (-6, -109).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 654 are 1, 2, 3, 6, 109, 218, 327, and 654.

• Prime factors: The factors which are prime numbers. For example, 2, 3, and 109 are prime factors of 654.

• 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 654 are (1, 654), (2, 327), etc.

• Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 654 is 2 × 3 × 109.

• Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number. For example, using multiplication to find factors of 654 like (2, 327).