Factors of 1254

The numbers that divide 1254 evenly are known as factors of 1254. A factor of 1254 is a number that divides the number without remainder. The factors of 1254 are 1, 2, 3, 6, 11, 17, 18, 22, 33, 34, 51, 66, 102, 187, 204, 374, 627, and 1254.

Negative factors of 1254: -1, -2, -3, -6, -11, -17, -18, -22, -33, -34, -51, -66, -102, -187, -204, -374, -627, and -1254.

Prime factors of 1254: 2, 3, 11, and 17.

Prime factorization of 1254: 2 × 3 × 11 × 17.

The sum of factors of 1254: 1 + 2 + 3 + 6 + 11 + 17 + 18 + 22 + 33 + 34 + 51 + 66 + 102 + 187 + 204 + 374 + 627 + 1254 = 3012

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 1254. Identifying the numbers which are multiplied to get the number 1254 is the multiplication method.

Step 1: Multiply 1254 by 1, 1254 × 1 = 1254.

Step 2: Check for other numbers that give 1254 after multiplying

2 × 627 = 1254

3 × 418 = 1254

6 × 209 = 1254

11 × 114 = 1254

17 × 74 = 1254

18 × 69 = 1254

22 × 57 = 1254

33 × 38 = 1254

Therefore, the positive factor pairs of 1254 are: (1, 1254), (2, 627), (3, 418), (6, 209), (11, 114), (17, 74), (18, 69), (22, 57), and (33, 38). 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 simple division method -

Step 1: Divide 1254 by 1, 1254 ÷ 1 = 1254.

Step 2: Continue dividing 1254 by the numbers until the remainder becomes 0.

1254 ÷ 1 = 1254

1254 ÷ 2 = 627

1254 ÷ 3 = 418

1254 ÷ 6 = 209

1254 ÷ 11 = 114

1254 ÷ 17 = 74

1254 ÷ 18 = 69

1254 ÷ 22 = 57

1254 ÷ 33 = 38

Therefore, the factors of 1254 are: 1, 2, 3, 6, 11, 17, 18, 22, 33, 38, 57, 69, 74, 114, 209, 418, 627, 1254.

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 1254 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1254 ÷ 2 = 627

627 ÷ 3 = 209

209 ÷ 11 = 19

19 ÷ 17 = 1

The prime factors of 1254 are 2, 3, 11, and 17. The prime factorization of 1254 is: 2 × 3 × 11 × 17.

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

Step 1: Firstly, 1254 is divided by 2 to get 627.

Step 2: Now divide 627 by 3 to get 209.

Step 3: Then divide 209 by 11 to get 19.

Step 4: Finally, divide 19 by 17 to get 1. Here, 17 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1254 is: 2 × 3 × 11 × 17.

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 1254: (1, 1254), (2, 627), (3, 418), (6, 209), (11, 114), (17, 74), (18, 69), (22, 57), and (33, 38).

• Negative factor pairs of 1254: (-1, -1254), (-2, -627), (-3, -418), (-6, -209), (-11, -114), (-17, -74), (-18, -69), (-22, -57), and (-33, -38).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1254 are 1, 2, 3, 6, 11, 17, 18, 22, 33, 38, 57, 69, 74, 114, 209, 418, 627, 1254.

• Prime factors: The factors which are prime numbers. For example, 2, 3, 11, and 17 are prime factors of 1254.

• 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 1254 are (1, 1254), (2, 627), etc.

• Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 1254 is 2 × 3 × 11 × 17.

• Multiplication method: A technique used to find factors by identifying pairs of numbers that can be multiplied to give the original number.