Factors of 650

The numbers that divide 650 evenly are known as factors of 650. A factor of 650 is a number that divides the number without remainder. The factors of 650 are 1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 325, and 650.

Negative factors of 650: -1, -2, -5, -10, -13, -25, -26, -50, -65, -130, -325, and -650.

Prime factors of 650: 2, 5, and 13.

Prime factorization of 650: 2 × 5² × 13.

The sum of factors of 650: 1 + 2 + 5 + 10 + 13 + 25 + 26 + 50 + 65 + 130 + 325 + 650 = 1302

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 650. Identifying the numbers that are multiplied to get the number 650 is the multiplication method.

Step 1: Multiply 650 by 1, 650 × 1 = 650.

Step 2: Check for other numbers that give 650 after multiplying:

2 × 325 = 650

5 × 130 = 650

10 × 65 = 650

13 × 50 = 650

25 × 26 = 650

Therefore, the positive factor pairs of 650 are: (1, 650), (2, 325), (5, 130), (10, 65), (13, 50), (25, 26). 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 in whole numbers as factors. Factors can be calculated by following the simple division method -

Step 1: Divide 650 by 1, 650 ÷ 1 = 650.

Step 2: Continue dividing 650 by the numbers until the remainder becomes 0.

650 ÷ 1 = 650

650 ÷ 2 = 325

650 ÷ 5 = 130

650 ÷ 10 = 65

650 ÷ 13 = 50

650 ÷ 25 = 26

Therefore, the factors of 650 are: 1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 325, 650.

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

650 ÷ 2 = 325

325 ÷ 5 = 65

65 ÷ 5 = 13

13 ÷ 13 = 1

The prime factors of 650 are 2, 5, and 13. The prime factorization of 650 is: 2 × 5² × 13.

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

Step 1: Firstly, 650 is divided by 2 to get 325.

Step 2: Now divide 325 by 5 to get 65.

Step 3: Then divide 65 by 5 to get 13. Here, 13 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 650 is: 2 × 5² × 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 650: (1, 650), (2, 325), (5, 130), (10, 65), (13, 50), and (25, 26).
• Negative factor pairs of 650: (-1, -650), (-2, -325), (-5, -130), (-10, -65), (-13, -50), and (-25, -26).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 650 are 1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 325, and 650.

• Prime factors: The factors which are prime numbers. For example, 2, 5, and 13 are prime factors of 650.

• 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 650 are (1, 650), (2, 325), etc.

• Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 650 is 2 × 5^2 × 13.

• Multiple: A number that can be divided by another number without leaving a remainder. For example, 650 is a multiple of 5.