Factors of 1569

The numbers that divide 1569 evenly are known as factors of 1569. A factor of 1569 is a number that divides the number without remainder. The factors of 1569 are 1, 3, 17, 27, 51, 89, 153, 267, 459, 523, and 1569.

Negative factors of 1569: -1, -3, -17, -27, -51, -89, -153, -267, -459, -523, and -1569.

Prime factors of 1569: 3, 17, and 31.

Prime factorization of 1569: 3 × 17 × 31.

The sum of factors of 1569: 1 + 3 + 17 + 27 + 51 + 89 + 153 + 267 + 459 + 523 + 1569 = 3159

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 1569. Identifying the numbers which are multiplied to get the number 1569 is the multiplication method.

Step 1: Multiply 1569 by 1, 1569 × 1 = 1569.

Step 2: Check for other numbers that give 1569 after multiplying

3 × 523 = 1569

17 × 92 = 1569

27 × 58 = 1569

51 × 31 = 1569

Therefore, the positive factor pairs of 1569 are: (1, 1569), (3, 523), (17, 92), (27, 58), (51, 31). All these factor pairs result in 1569. 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 the simple division method -

Step 1: Divide 1569 by 1, 1569 ÷ 1 = 1569.

Step 2: Continue dividing 1569 by the numbers until the remainder becomes 0.

1569 ÷ 1 = 1569

1569 ÷ 3 = 523

1569 ÷ 17 = 92

1569 ÷ 27 = 58

1569 ÷ 51 = 31

Therefore, the factors of 1569 are: 1, 3, 17, 27, 51, 89, 153, 267, 459, 523, 1569.

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 1569 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1569 ÷ 3 = 523

523 ÷ 17 = 31

31 ÷ 31 = 1

The prime factors of 1569 are 3, 17, and 31. The prime factorization of 1569 is: 3 × 17 × 31.

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

Step 1: Firstly, 1569 is divided by 3 to get 523.

Step 2: Now divide 523 by 17 to get 31.

Step 3: Divide 31 by 31 to get 1. Here, 31 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 1569 is: 3 × 17 × 31.

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 1569: (1, 1569), (3, 523), (17, 92), (27, 58), and (51, 31).

• Negative factor pairs of 1569: (-1, -1569), (-3, -523), (-17, -92), (-27, -58), and (-51, -31).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1569 are 1, 3, 17, 27, 51, 89, 153, 267, 459, 523, and 1569.

• Prime factors: The factors which are prime numbers. For example, 3, 17, and 31 are prime factors of 1569.

• 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 1569 are (1, 1569), (3, 523), etc.

• Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 1569 is 3 × 17 × 31.

• Multiplication method: A method of finding factors by identifying pairs of numbers that multiply to give the original number. For example, using the multiplication method for 1569 gives pairs like (3, 523).