Factors of 1548

The numbers that divide 1548 evenly are known as factors of 1548. A factor of 1548 is a number that divides the number without remainder. The factors of 1548 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 49, 63, 84, 98, 126, 147, 196, 294, 441, 588, 772, and 1548.

Negative factors of 1548: -1, -2, -3, -4, -6, -7, -9, -12, -14, -18, -21, -28, -36, -42, -49, -63, -84, -98, -126, -147, -196, -294, -441, -588, -772, and -1548.

Prime factors of 1548: 2, 3, and 7.

Prime factorization of 1548: 2² × 3 × 7² × 3.

The sum of factors of 1548: 1 + 2 + 3 + 4 + 6 + 7 + 9 + 12 + 14 + 18 + 21 + 28 + 36 + 42 + 49 + 63 + 84 + 98 + 126 + 147 + 196 + 294 + 441 + 588 + 772 + 1548 = 5040

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 1548. Identifying the numbers which are multiplied to get the number 1548 is the multiplication method.

Step 1: Multiply 1548 by 1, 1548 × 1 = 1548.

Step 2: Check for other numbers that give 1548 after multiplying

2 × 774 = 1548

3 × 516 = 1548

4 × 387 = 1548

6 × 258 = 1548

7 × 221 = 1548

9 × 172 = 1548

12 × 129 = 1548

14 × 111 = 1548

18 × 86 = 1548

21 × 74 = 1548

28 × 55 = 1548

36 × 43 = 1548

Therefore, the positive factor pairs of 1548 are: (1, 1548), (2, 774), (3, 516), (4, 387), (6, 258), (7, 221), (9, 172), (12, 129), (14, 111), (18, 86), (21, 74), (28, 55), and (36, 43). For every positive factor, there is a negative factor.

Dividing the given numbers with 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 1548 by 1, 1548 ÷ 1 = 1548.

Step 2: Continue dividing 1548 by the numbers until the remainder becomes 0.

1548 ÷ 1 = 1548

1548 ÷ 2 = 774

1548 ÷ 3 = 516

1548 ÷ 4 = 387

1548 ÷ 6 = 258

1548 ÷ 7 = 221

1548 ÷ 9 = 172

1548 ÷ 12 = 129

1548 ÷ 14 = 111

1548 ÷ 18 = 86

1548 ÷ 21 = 74

1548 ÷ 28 = 55

1548 ÷ 36 = 43

Therefore, the factors of 1548 are: 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 43, 55, 74, 86, 111, 129, 172, 221, 258, 387, 516, 774, 1548.

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 1548 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1548 ÷ 2 = 774

774 ÷ 2 = 387

387 ÷ 3 = 129

129 ÷ 3 = 43

43 is a prime number and cannot be divided further. The prime factors of 1548 are 2, 3, and 7. The prime factorization of 1548 is: 2² × 3 × 43.

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

Step 1: Firstly, 1548 is divided by 2 to get 774.

Step 2: Now divide 774 by 2 to get 387.

Step 3: Then divide 387 by 3 to get 129.

Step 4: Divide 129 by 3 to get 43. Here, 43 is a prime number that cannot be divided anymore. So, the prime factorization of 1548 is: 2² × 3 × 43.

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 1548: (1, 1548), (2, 774), (3, 516), (4, 387), (6, 258), (7, 221), (9, 172), (12, 129), (14, 111), (18, 86), (21, 74), (28, 55), and (36, 43).

• Negative factor pairs of 1548: (-1, -1548), (-2, -774), (-3, -516), (-4, -387), (-6, -258), (-7, -221), (-9, -172), (-12, -129), (-14, -111), (-18, -86), (-21, -74), (-28, -55), and (-36, -43).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1548 are 1, 2, 3, etc.

• Prime factors: The factors which are prime numbers. For example, 2, 3, and 43 are prime factors of 1548.

• 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 1548 are (1, 1548), (2, 774), etc.

• Prime factorization: Expressing a number as a product of its prime factors. For example, 1548 = 2² × 3 × 43.

• Negative factors: Factors of a number that are negative. For example, -1, -2, -3, etc., are negative factors of 1548.