Factors of 649

The numbers that divide 649 evenly are known as factors of 649. A factor of 649 is a number that divides the number without remainder. The factors of 649 are 1, 17, 38, and 649.

Negative factors of 649: -1, -17, -38, and -649.

Prime factors of 649: 17 and 38.

Prime factorization of 649: 17 × 38.

The sum of factors of 649: 1 + 17 + 38 + 649 = 705

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 649. Identifying the numbers which are multiplied to get the number 649 is the multiplication method.

Step 1: Multiply 649 by 1, 649 × 1 = 649.

Step 2: Check for other numbers that give 649 after multiplying 17 × 38 = 649

Therefore, the positive factor pairs of 649 are: (1, 649) and (17, 38). All these factor pairs result in 649. 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 649 by 1, 649 ÷ 1 = 649.

Step 2: Continue dividing 649 by the numbers until the remainder becomes 0.

649 ÷ 1 = 649

649 ÷ 17 = 38

649 ÷ 38 = 17

Therefore, the factors of 649 are: 1, 17, 38, and 649.

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

649 ÷ 17 = 38

38 ÷ 38 = 1

The prime factors of 649 are 17 and 38. The prime factorization of 649 is: 17 × 38.

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

Step 1: Firstly, 649 is divided by 17 to get 38.

Step 2: Now divide 38 by 38 to get 1. So, the prime factorization of 649 is: 17 × 38.

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 649: (1, 649) and (17, 38).
• Negative factor pairs of 649: (-1, -649) and (-17, -38).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 649 are 1, 17, 38, and 649.

• Prime factors: The factors which are prime numbers. For example, 17 and 38 are prime factors of 649.

• 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 649 are (1, 649) and (17, 38).

• Prime Factorization: The process of expressing a number as the product of its prime factors. For 649, it is 17 × 38.

• Negative factors: Factors that are negative, such as -1, -17, -38, and -649 for the number 649.