Factors of 1420

The numbers that divide 1420 evenly are known as factors of 1420.

A factor of 1420 is a number that divides the number without remainder.

The factors of 1420 are 1, 2, 4, 5, 10, 20, 71, 142, 284, 355, 710, and 1420.

Negative factors of 1420: -1, -2, -4, -5, -10, -20, -71, -142, -284, -355, -710, and -1420.

Prime factors of 1420: 2, 5, and 71.

Prime factorization of 1420: 2² × 5 × 71.

The sum of factors of 1420: 1 + 2 + 4 + 5 + 10 + 20 + 71 + 142 + 284 + 355 + 710 + 1420 = 3024

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 1420. Identifying the numbers which are multiplied to get the number 1420 is the multiplication method.

Step 1: Multiply 1420 by 1, 1420 × 1 = 1420.

Step 2: Check for other numbers that give 1420 after multiplying

2 × 710 = 1420

4 × 355 = 1420

5 × 284 = 1420

10 × 142 = 1420

20 × 71 = 1420

Therefore, the positive factor pairs of 1420 are: (1, 1420), (2, 710), (4, 355), (5, 284), (10, 142), (20, 71).

All these factor pairs result in 1420.

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 1420 by 1, 1420 ÷ 1 = 1420.

Step 2: Continue dividing 1420 by the numbers until the remainder becomes 0.

1420 ÷ 1 = 1420

1420 ÷ 2 = 710

1420 ÷ 4 = 355

1420 ÷ 5 = 284

1420 ÷ 10 = 142

1420 ÷ 20 = 71

Therefore, the factors of 1420 are: 1, 2, 4, 5, 10, 20, 71, 142, 284, 355, 710, 1420.

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 1420 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1420 ÷ 2 = 710

710 ÷ 2 = 355

355 ÷ 5 = 71

71 ÷ 71 = 1

The prime factors of 1420 are 2, 5, and 71. The prime factorization of 1420 is: 2² × 5 × 71.

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

Step 1: Firstly, 1420 is divided by 2 to get 710.

Step 2: Now divide 710 by 2 to get 355.

Step 3: Then divide 355 by 5 to get 71. Here, 71 is the smallest prime number, that cannot be divided anymore.

So, the prime factorization of 1420 is: 2² × 5 × 71.

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 1420: (1, 1420), (2, 710), (4, 355), (5, 284), (10, 142), and (20, 71).

Negative factor pairs of 1420: (-1, -1420), (-2, -710), (-4, -355), (-5, -284), (-10, -142), and (-20, -71).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1420 are 1, 2, 4, 5, 10, 20, 71, 142, 284, 355, 710, and 1420.

• Prime factors: The factors which are prime numbers. For example, 2, 5, and 71 are prime factors of 1420.

• 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 1420 are (1, 1420), (2, 710), etc.

• Prime factorization: Expressing a number as the product of its prime factors. For instance, the prime factorization of 1420 is 2² × 5 × 71.

• Multiple: A number that can be divided by another number without a remainder. For example, 1420 is a multiple of 4.