Factors of 1260

The numbers that divide 1260 evenly are known as factors of 1260. A factor of 1260 is a number that divides the number without remainder. The factors of 1260 are 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630, and 1260.

Negative factors of 1260: -1, -2, -3, -4, -5, -6, -7, -9, -10, -12, -14, -15, -18, -20, -21, -28, -30, -35, -36, -42, -45, -60, -63, -70, -84, -90, -105, -126, -140, -180, -210, -252, -315, -420, -630, and -1260.

Prime factors of 1260: 2, 3, 5, and 7.

Prime factorization of 1260: 2² × 3² × 5 × 7.

The sum of factors of 1260: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 9 + 10 + 12 + 14 + 15 + 18 + 20 + 21 + 28 + 30 + 35 + 36 + 42 + 45 + 60 + 63 + 70 + 84 + 90 + 105 + 126 + 140 + 180 + 210 + 252 + 315 + 420 + 630 + 1260 = 4032

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 1260. Identifying the numbers which are multiplied to get the number 1260 is the multiplication method.

Step 1: Multiply 1260 by 1, 1260 × 1 = 1260.

Step 2: Check for other numbers that give 1260 after multiplying

2 × 630 = 1260

3 × 420 = 1260

4 × 315 = 1260

5 × 252 = 1260

6 × 210 = 1260

7 × 180 = 1260

9 × 140 = 1260

10 × 126 = 1260

12 × 105 = 1260

14 × 90 = 1260

15 × 84 = 1260

18 × 70 = 1260

20 × 63 = 1260

21 × 60 = 1260

28 × 45 = 1260

30 × 42 = 1260

35 × 36 = 1260

Therefore, the positive factor pairs of 1260 are: (1, 1260), (2, 630), (3, 420), (4, 315), (5, 252), (6, 210), (7, 180), (9, 140), (10, 126), (12, 105), (14, 90), (15, 84), (18, 70), (20, 63), (21, 60), (28, 45), and (30, 42). All these factor pairs result in 1260. 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 1260 by 1, 1260 ÷ 1 = 1260.

Step 2: Continue dividing 1260 by the numbers until the remainder becomes 0.

1260 ÷ 1 = 1260

1260 ÷ 2 = 630

1260 ÷ 3 = 420

1260 ÷ 4 = 315

1260 ÷ 5 = 252

1260 ÷ 6 = 210

1260 ÷ 7 = 180

1260 ÷ 9 = 140

1260 ÷ 10 = 126

1260 ÷ 12 = 105

1260 ÷ 14 = 90

1260 ÷ 15 = 84

1260 ÷ 18 = 70

1260 ÷ 20 = 63

1260 ÷ 21 = 60

1260 ÷ 28 = 45

1260 ÷ 30 = 42

Therefore, the factors of 1260 are: 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630, and 1260.

The factors can be found by dividing it with a prime number. 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 1260 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1260 ÷ 2 = 630

630 ÷ 2 = 315

315 ÷ 3 = 105

105 ÷ 3 = 35

35 ÷ 5 = 7

7 ÷ 7 = 1

The prime factors of 1260 are 2, 3, 5, and 7. The prime factorization of 1260 is: 2² × 3² × 5 × 7.

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

Step 1: Firstly, 1260 is divided by 2 to get 630.

Step 2: Now divide 630 by 2 to get 315.

Step 3: Then divide 315 by 3 to get 105.

Step 4: Divide 105 by 3 to get 35.

Step 5: Divide 35 by 5 to get 7. Here, 7 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1260 is: 2² × 3² × 5 × 7.

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 1260: (1, 1260), (2, 630), (3, 420), (4, 315), (5, 252), (6, 210), (7, 180), (9, 140), (10, 126), (12, 105), (14, 90), (15, 84), (18, 70), (20, 63), (21, 60), (28, 45), and (30, 42).

• Negative factor pairs of 1260: (-1, -1260), (-2, -630), (-3, -420), (-4, -315), (-5, -252), (-6, -210), (-7, -180), (-9, -140), (-10, -126), (-12, -105), (-14, -90), (-15, -84), (-18, -70), (-20, -63), (-21, -60), (-28, -45), and (-30, -42).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1260 are 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630, and 1260.

• Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 7 are prime factors of 1260.

• 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 1260 are (1, 1260), (2, 630), etc.

• Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 1260 is 2² × 3² × 5 × 7.

• Multiplication method: Finding factors by identifying pairs of numbers that multiply to give the original number. For example, using multiplication to find factors of 1260 involves pairing numbers like 2 and 630.