Factors of 1251

The numbers that divide 1251 evenly are known as factors of 1251. A factor of 1251 is a number that divides the number without remainder. The factors of 1251 are 1, 3, 11, 33, 37, 111, 407, and 1251.

Negative factors of 1251: -1, -3, -11, -33, -37, -111, -407, and -1251.

Prime factors of 1251: 3, 11, and 37.

Prime factorization of 1251: 3 × 11 × 37.

The sum of factors of 1251: 1 + 3 + 11 + 33 + 37 + 111 + 407 + 1251 = 1854

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 1251. Identifying the numbers which are multiplied to get the number 1251 is the multiplication method.

Step 1: Multiply 1251 by 1, 1251 × 1 = 1251.

Step 2: Check for other numbers that give 1251 after multiplying

3 × 417 = 1251

11 × 113.727 ≠ 1251 (since 113.727 is not an integer, this is not a factor)

37 × 33.8108 ≠ 1251 (since 33.8108 is not an integer, this is not a factor)

Therefore, the positive factor pairs of 1251 are: (1, 1251), (3, 417), and (11, 113). All these factor pairs result in 1251. 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 1251 by 1, 1251 ÷ 1 = 1251.

Step 2: Continue dividing 1251 by the numbers until the remainder becomes 0.

1251 ÷ 1 = 1251

1251 ÷ 3 = 417

1251 ÷ 11 = 113.727 (not a whole number)

1251 ÷ 37 = 33.8108 (not a whole number)

Therefore, the factors of 1251 are: 1, 3, 11, 33, 37, 111, 407, 1251.

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 1251 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1251 ÷ 3 = 417

417 ÷ 11 = 37

37 ÷ 37 = 1

The prime factors of 1251 are 3, 11, and 37. The prime factorization of 1251 is: 3 × 11 × 37.

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

Step 1: Firstly, 1251 is divided by 3 to get 417.

Step 2: Now divide 417 by 11 to get 37.

Step 3: Then divide 37 by 37 to get 1. So, the prime factorization of 1251 is: 3 × 11 × 37.

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 1251: (1, 1251), (3, 417), and (11, 113).

• Negative factor pairs of 1251: (-1, -1251), (-3, -417), and (-11, -113).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1251 are 1, 3, 11, 33, 37, 111, 407, and 1251.

• Prime factors: The factors which are prime numbers. For example, 3, 11, and 37 are prime factors of 1251.

• 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 1251 are (1, 1251), (3, 417), and (11, 113).

• Prime factorization: The expression of a number as a product of its prime factors. For example, 1251 can be expressed as 3 × 11 × 37.

• Multiplication method: A method used to find factors by identifying pairs of numbers that multiply to give the original number. For example, identifying (3, 417) as a factor pair of 1251.