Factors of 1564

The numbers that divide 1564 evenly are known as factors of 1564. A factor of 1564 is a number that divides the number without remainder. The factors of 1564 are 1, 2, 4, 17, 23, 34, 46, 68, 92, 391, 782, and 1564.

Negative factors of 1564: -1, -2, -4, -17, -23, -34, -46, -68, -92, -391, -782, and -1564.

Prime factors of 1564: 2, 17, and 23.

Prime factorization of 1564: 2 × 2 × 17 × 23.

The sum of factors of 1564: 1 + 2 + 4 + 17 + 23 + 34 + 46 + 68 + 92 + 391 + 782 + 1564 = 3024

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 1564. Identifying the numbers which are multiplied to get the number 1564 is the multiplication method.

Step 1: Multiply 1564 by 1, 1564 × 1 = 1564.

Step 2: Check for other numbers that give 1564 after multiplying

2 × 782 = 1564

4 × 391 = 1564

17 × 92 = 1564

23 × 68 = 1564

Therefore, the positive factor pairs of 1564 are: (1, 1564), (2, 782), (4, 391), (17, 92), (23, 68). 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 1564 by 1, 1564 ÷ 1 = 1564.

Step 2: Continue dividing 1564 by the numbers until the remainder becomes 0.

1564 ÷ 1 = 1564

1564 ÷ 2 = 782

1564 ÷ 4 = 391

1564 ÷ 17 = 92

1564 ÷ 23 = 68

Therefore, the factors of 1564 are: 1, 2, 4, 17, 23, 34, 46, 68, 92, 391, 782, 1564.

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 1564 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1564 ÷ 2 = 782

782 ÷ 2 = 391

391 ÷ 17 = 23

23 ÷ 23 = 1

The prime factors of 1564 are 2, 17, and 23. The prime factorization of 1564 is: 2 × 2 × 17 × 23.

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

Step 1: Firstly, 1564 is divided by 2 to get 782.

Step 2: Now divide 782 by 2 to get 391.

Step 3: Then divide 391 by 17 to get 23.

Step 4: Divide 23 by 23 to get 1. So, the prime factorization of 1564 is: 2 × 2 × 17 × 23.

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 1564: (1, 1564), (2, 782), (4, 391), (17, 92), and (23, 68).

• Negative factor pairs of 1564: (-1, -1564), (-2, -782), (-4, -391), (-17, -92), and (-23, -68).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1564 are 1, 2, 4, 17, 23, 34, 46, 68, 92, 391, 782, and 1564.

• Prime factors: The factors which are prime numbers. For example, 2, 17, and 23 are prime factors of 1564.

• 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 1564 are (1, 1564), (2, 782), etc.

• Prime factorization: The expression representing a number as a product of its prime factors. For example, 1564 = 2 × 2 × 17 × 23.

• Multiplication method: A method to find factors by identifying number pairs that multiply to give the original number.