Factors of 1248

The numbers that divide 1248 evenly are known as factors of 1248. A factor of 1248 is a number that divides the number without remainder. The factors of 1248 are 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 208, 312, 416, 624, and 1248.

Negative factors of 1248: -1, -2, -3, -4, -6, -8, -12, -13, -16, -24, -26, -39, -48, -52, -78, -104, -156, -208, -312, -416, -624, and -1248.

Prime factors of 1248: 2 and 3, 13.

Prime factorization of 1248: 2⁴ × 3 × 13.

The sum of factors of 1248: 1 + 2 + 3 + 4 + 6 + 8 + 12 + 13 + 16 + 24 + 26 + 39 + 48 + 52 + 78 + 104 + 156 + 208 + 312 + 416 + 624 + 1248 = 3408

Factors can be found using different methods. Mentioned below are some commonly used methods:

• Finding factors using multiplication
• Finding factors using division method
• Prime factors and Prime factorization

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 1248. Identifying the numbers which are multiplied to get the number 1248 is the multiplication method.

Step 1: Multiply 1248 by 1, 1248 × 1 = 1248.

Step 2: Check for other numbers that give 1248 after multiplying

2 × 624 = 1248

3 × 416 = 1248

4 × 312 = 1248

6 × 208 = 1248

8 × 156 = 1248

12 × 104 = 1248

13 × 96 = 1248

16 × 78 = 1248

24 × 52 = 1248

26 × 48 = 1248

39 × 32 = 1248

Therefore, the positive factor pairs of 1248 are: (1, 1248), (2, 624), (3, 416), (4, 312), (6, 208), (8, 156), (12, 104), (13, 96), (16, 78), (24, 52), (26, 48), (32, 39). 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 a whole numbers as factors. Factors can be calculated by following a simple division method -

Step 1: Divide 1248 by 1, 1248 ÷ 1 = 1248.

Step 2: Continue dividing 1248 by the numbers until the remainder becomes 0.

1248 ÷ 1 = 1248

1248 ÷ 2 = 624

1248 ÷ 3 = 416

1248 ÷ 4 = 312

1248 ÷ 6 = 208

1248 ÷ 8 = 156

1248 ÷ 12 = 104

1248 ÷ 13 = 96

1248 ÷ 16 = 78

1248 ÷ 24 = 52

1248 ÷ 26 = 48

1248 ÷ 32 = 39

Therefore, the factors of 1248 are: 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 32, 39, 48, 52, 78, 96, 104, 156, 208, 312, 416, 624, 1248.

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 1248 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.

1248 ÷ 2 = 624

624 ÷ 2 = 312

312 ÷ 2 = 156

156 ÷ 2 = 78

78 ÷ 2 = 39

39 ÷ 3 = 13

13 ÷ 13 = 1

The prime factors of 1248 are 2, 3, and 13. The prime factorization of 1248 is: 2^4 × 3 × 13.

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

Step 1: Firstly, 1248 is divided by 2 to get 624.

Step 2: Now divide 624 by 2 to get 312.

Step 3: Then divide 312 by 2 to get 156.

Step 4: Divide 156 by 2 to get 78.

Step 5: Divide 78 by 2 to get 39.

Step 6: Divide 39 by 3 to get 13. Here, 13 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1248 is: 2⁴ × 3 × 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 1248: (1, 1248), (2, 624), (3, 416), (4, 312), (6, 208), (8, 156), (12, 104), (13, 96), (16, 78), (24, 52), (26, 48), (32, 39).

• Negative factor pairs of 1248: (-1, -1248), (-2, -624), (-3, -416), (-4, -312), (-6, -208), (-8, -156), (-12, -104), (-13, -96), (-16, -78), (-24, -52), (-26, -48), (-32, -39).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1248 are 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 32, 39, 48, 52, 78, 96, 104, 156, 208, 312, 416, 624, and 1248.

• Prime factors: The factors which are prime numbers. For example, 2, 3, and 13 are prime factors of 1248.

• 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 1248 are (1, 1248), (2, 624), etc.

• Prime factorization: The process of expressing a number as the product of its prime factors. For 1248, it is 2⁴ × 3 × 13.

• Multiples: The result of multiplying a number by an integer. For example, 1248 is a multiple of 4.