Factors of 1560

The numbers that divide 1560 evenly are known as factors of 1560. A factor of 1560 is a number that divides the number without remainder. The factors of 1560 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 20, 24, 26, 30, 39, 40, 52, 60, 65, 78, 104, 120, 130, 156, 195, 260, 312, 390, 520, 780, and 1560.

Negative factors of 1560: -1, -2, -3, -4, -5, -6, -8, -10, -12, -13, -15, -20, -24, -26, -30, -39, -40, -52, -60, -65, -78, -104, -120, -130, -156, -195, -260, -312, -390, -520, -780, and -1560.

Prime factors of 1560: 2, 3, 5, and 13.

Prime factorization of 1560: 2³ × 3 × 5 × 13.

The sum of factors of 1560: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 13 + 15 + 20 + 24 + 26 + 30 + 39 + 40 + 52 + 60 + 65 + 78 + 104 + 120 + 130 + 156 + 195 + 260 + 312 + 390 + 520 + 780 + 1560 = 5084

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 1560. Identifying the numbers which are multiplied to get the number 1560 is the multiplication method.

Step 1: Multiply 1560 by 1, 1560 × 1 = 1560.

Step 2: Check for other numbers that give 1560 after multiplying

2 × 780 = 1560

3 × 520 = 1560

4 × 390 = 1560

5 × 312 = 1560

6 × 260 = 1560

8 × 195 = 1560

10 × 156 = 1560

12 × 130 = 1560

13 × 120 = 1560

15 × 104 = 1560

20 × 78 = 1560

24 × 65 = 1560

26 × 60 = 1560

30 × 52 = 1560

39 × 40 = 1560

Therefore, the positive factor pairs of 1560 are: (1, 1560), (2, 780), (3, 520), (4, 390), (5, 312), (6, 260), (8, 195), (10, 156), (12, 130), (13, 120), (15, 104), (20, 78), (24, 65), (26, 60), (30, 52), (39, 40). 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 1560 by 1, 1560 ÷ 1 = 1560.

Step 2: Continue dividing 1560 by the numbers until the remainder becomes 0.

1560 ÷ 1 = 1560

1560 ÷ 2 = 780

1560 ÷ 3 = 520

1560 ÷ 4 = 390

1560 ÷ 5 = 312

1560 ÷ 6 = 260

1560 ÷ 8 = 195

1560 ÷ 10 = 156

1560 ÷ 12 = 130

1560 ÷ 13 = 120

1560 ÷ 15 = 104

1560 ÷ 20 = 78

1560 ÷ 24 = 65

1560 ÷ 26 = 60

1560 ÷ 30 = 52

1560 ÷ 39 = 40

Therefore, the factors of 1560 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 20, 24, 26, 30, 39, 40, 52, 60, 65, 78, 104, 120, 130, 156, 195, 260, 312, 390, 520, 780, and 1560.

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 1560 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1560 ÷ 2 = 780

780 ÷ 2 = 390

390 ÷ 2 = 195

195 ÷ 3 = 65

65 ÷ 5 = 13

13 ÷ 13 = 1

The prime factors of 1560 are 2, 3, 5, and 13. The prime factorization of 1560 is: 2³ × 3 × 5 × 13.

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

Step 1: Firstly, 1560 is divided by 2 to get 780.

Step 2: Now divide 780 by 2 to get 390.

Step 3: Then divide 390 by 2 to get 195.

Step 4: Divide 195 by 3 to get 65.

Step 5: Divide 65 by 5 to get 13. Here, 13 is a prime number that cannot be divided anymore. So, the prime factorization of 1560 is: 2³ × 3 × 5 × 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 1560: (1, 1560), (2, 780), (3, 520), (4, 390), (5, 312), (6, 260), (8, 195), (10, 156), (12, 130), (13, 120), (15, 104), (20, 78), (24, 65), (26, 60), (30, 52), (39, 40).

• Negative factor pairs of 1560: (-1, -1560), (-2, -780), (-3, -520), (-4, -390), (-5, -312), (-6, -260), (-8, -195), (-10, -156), (-12, -130), (-13, -120), (-15, -104), (-20, -78), (-24, -65), (-26, -60), (-30, -52), (-39, -40).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1560 are 1, 2, 3, 4, 5, etc.

• Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 13 are prime factors of 1560.

• Prime factorization: Breaking down a number into its prime factors. For 1560, it is 2³ × 3 × 5 × 13.

• 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 1560 are (1, 1560), (2, 780), etc.

• Multiple: A number that can be divided by another number without a remainder. For example, 1560 is a multiple of 13.