Factors of 1744

The numbers that divide 1744 evenly are known as factors of 1744.

A factor of 1744 is a number that divides the number without a remainder.

The factors of 1744 are 1, 2, 4, 8, 16, 109, 218, 436, 872, and 1744.

Negative factors of 1744: -1, -2, -4, -8, -16, -109, -218, -436, -872, and -1744.

Prime factors of 1744: 2 and 109.

Prime factorization of 1744: 2³ × 109.

The sum of factors of 1744: 1 + 2 + 4 + 8 + 16 + 109 + 218 + 436 + 872 + 1744 = 3410

Factors can be found using different methods. Mentioned below are some commonly used methods:

• Finding factors using multiplication
• Finding factors using the division method
• Prime factors and Prime factorization

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 1744. Identifying the numbers which are multiplied to get the number 1744 is the multiplication method.

Step 1: Multiply 1744 by 1, 1744 × 1 = 1744.

Step 2: Check for other numbers that give 1744 after multiplying

2 × 872 = 1744

4 × 436 = 1744

8 × 218 = 1744

16 × 109 = 1744

Therefore, the positive factor pairs of 1744 are: (1, 1744), (2, 872), (4, 436), (8, 218), (16, 109).

All these factor pairs result in 1744.

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 1744 by 1, 1744 ÷ 1 = 1744.

Step 2: Continue dividing 1744 by the numbers until the remainder becomes 0.

1744 ÷ 1 = 1744

1744 ÷ 2 = 872

1744 ÷ 4 = 436

1744 ÷ 8 = 218

1744 ÷ 16 = 109

Therefore, the factors of 1744 are: 1, 2, 4, 8, 16, 109, 218, 436, 872, 1744.

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 1744 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1744 ÷ 2 = 872

872 ÷ 2 = 436

436 ÷ 2 = 218

218 ÷ 2 = 109

109 ÷ 109 = 1

The prime factors of 1744 are 2 and 109.

The prime factorization of 1744 is: 2³ × 109.

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

Step 1: Firstly, 1744 is divided by 2 to get 872.

Step 2: Now divide 872 by 2 to get 436.

Step 3: Then divide 436 by 2 to get 218.

Step 4: Divide 218 by 2 to get 109. Here, 109 is the smallest prime number that cannot be divided anymore.

So, the prime factorization of 1744 is: 2³ × 109.

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 1744: (1, 1744), (2, 872), (4, 436), (8, 218), and (16, 109).

Negative factor pairs of 1744: (-1, -1744), (-2, -872), (-4, -436), (-8, -218), and (-16, -109).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1744 are 1, 2, 4, 8, 16, 109, 218, 436, 872, and 1744.

• Prime factors: The factors which are prime numbers. For example, 2 and 109 are prime factors of 1744.

• 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 1744 are (1, 1744), (2, 872), etc.

• Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 1744 is 2³ × 109.

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