Factors of 1424

The numbers that divide 1424 evenly are known as factors of 1424.

A factor of 1424 is a number that divides the number without remainder.

The factors of 1424 are 1, 2, 4, 8, 16, 89, 178, 356, 712, and 1424.

Negative factors of 1424: -1, -2, -4, -8, -16, -89, -178, -356, -712, and -1424.

Prime factors of 1424: 2 and 89.

Prime factorization of 1424: 2⁴ × 89.

The sum of factors of 1424: 1 + 2 + 4 + 8 + 16 + 89 + 178 + 356 + 712 + 1424 = 2790

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

• Finding factors using multiplication
• Finding factors using 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 1424. Identifying the numbers which are multiplied to get the number 1424 is the multiplication method.

Step 1: Multiply 1424 by 1, 1424 × 1 = 1424.

Step 2: Check for other numbers that give 1424 after multiplying     

2 × 712 = 1424    

 4 × 356 = 1424     

8 × 178 = 1424     

16 × 89 = 1424

Therefore, the positive factor pairs of 1424 are: (1, 1424), (2, 712), (4, 356), (8, 178), (16, 89).

All these factor pairs result in 1424.

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 1424 by 1, 1424 ÷ 1 = 1424.

Step 2: Continue dividing 1424 by the numbers until the remainder becomes 0.

1424 ÷ 1 = 1424

1424 ÷ 2 = 712

1424 ÷ 4 = 356

1424 ÷ 8 = 178

1424 ÷ 16 = 89

Therefore, the factors of 1424 are: 1, 2, 4, 8, 16, 89, 178, 356, 712, 1424.

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 1424 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1424 ÷ 2 = 712

712 ÷ 2 = 356

356 ÷ 2 = 178

178 ÷ 2 = 89

89 ÷ 89 = 1

The prime factors of 1424 are 2 and 89.

The prime factorization of 1424 is: 2⁴ × 89.

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

Step 1: Firstly, 1424 is divided by 2 to get 712.

Step 2: Now divide 712 by 2 to get 356.

Step 3: Then divide 356 by 2 to get 178.

Step 4: Divide 178 by 2 to get 89. Here, 89 is the smallest prime number that cannot be divided anymore.

So, the prime factorization of 1424 is: 2⁴ × 89.

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 1424: (1, 1424), (2, 712), (4, 356), (8, 178), and (16, 89).

Negative factor pairs of 1424: (-1, -1424), (-2, -712), (-4, -356), (-8, -178), and (-16, -89).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1424 are 1, 2, 4, 8, 16, 89, 178, 356, 712, and 1424.

• Prime factors: The factors which are prime numbers. For example, 2 and 89 are prime factors of 1424.

• 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 1424 are (1, 1424), (2, 712), etc.

• Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 1424 is 2⁴ × 89.

• Negative factors: Factors that are negative can be derived from the positive factors. For example, -1, -2, -4, etc., are negative factors of 1424.