Factors of 1224

The numbers that divide 1224 evenly are known as factors of 1224. A factor of 1224 is a number that divides the number without remainder. The factors of 1224 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 289, 408, 578, 612, and 1224.

Negative factors of 1224: -1, -2, -3, -4, -6, -8, -12, -17, -24, -34, -51, -68, -102, -136, -204, -289, -408, -578, -612, and -1224.

Prime factors of 1224: 2, 3, and 17.

Prime factorization of 1224: 2³ × 3 × 17².

The sum of factors of 1224: 1 + 2 + 3 + 4 + 6 + 8 + 12 + 17 + 24 + 34 + 51 + 68 + 102 + 136 + 204 + 289 + 408 + 578 + 612 + 1224 = 3774

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 1224. Identifying the numbers which are multiplied to get the number 1224 is the multiplication method.

Step 1: Multiply 1224 by 1, 1224 × 1 = 1224.

Step 2: Check for other numbers that give 1224 after multiplying

2 × 612 = 1224

3 × 408 = 1224

4 × 306 = 1224

6 × 204 = 1224

8 × 153 = 1224

12 × 102 = 1224

17 × 72 = 1224

24 × 51 = 1224

34 × 36 = 1224

Therefore, the positive factor pairs of 1224 are: (1, 1224), (2, 612), (3, 408), (4, 306), (6, 204), (8, 153), (12, 102), (17, 72), (24, 51), and (34, 36). 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 1224 by 1, 1224 ÷ 1 = 1224.

Step 2: Continue dividing 1224 by the numbers until the remainder becomes 0.

1224 ÷ 1 = 1224

1224 ÷ 2 = 612

1224 ÷ 3 = 408

1224 ÷ 4 = 306

1224 ÷ 6 = 204

1224 ÷ 8 = 153

1224 ÷ 12 = 102

1224 ÷ 17 = 72

1224 ÷ 24 = 51

1224 ÷ 34 = 36

Therefore, the factors of 1224 are: 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 289, 408, 578, 612, 1224.

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 1224 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1224 ÷ 2 = 612

612 ÷ 2 = 306

306 ÷ 2 = 153

153 ÷ 3 = 51

51 ÷ 3 = 17

17 ÷ 17 = 1

The prime factors of 1224 are 2, 3, and 17. The prime factorization of 1224 is: 2³ × 3 × 17².

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

Step 1: Firstly, 1224 is divided by 2 to get 612.

Step 2: Now divide 612 by 2 to get 306.

Step 3: Then divide 306 by 2 to get 153.

Step 4: Divide 153 by 3 to get 51. Step 5: Divide 51 by 3 to get 17. Here, 17 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 1224 is: 2³ × 3 × 17².

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 1224: (1, 1224), (2, 612), (3, 408), (4, 306), (6, 204), (8, 153), (12, 102), (17, 72), (24, 51), and (34, 36).
• Negative factor pairs of 1224: (-1, -1224), (-2, -612), (-3, -408), (-4, -306), (-6, -204), (-8, -153), (-12, -102), (-17, -72), (-24, -51), and (-34, -36).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1224 are 1, 2, 3, 4, 6, etc.

• Prime Factors: The factors which are prime numbers. For example, 2, 3, and 17 are prime factors of 1224.

• 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 1224 are (1, 1224), (2, 612), etc.

• Multiplication Method: A method to find factors by identifying pairs of numbers that multiply to give the target number.

• Division Method: A method to find factors by dividing the number by whole numbers until the remainder is zero.