# Factors of 1420

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

#### How to find factors of a number

 1.   Find factors of 1420 using Division Method 2.   Find factors of 1420 using Prime Factorization 3.   Find factors of 1420 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 1420

• Divide 1420 by 1: 1420 ÷ 1 : Remainder = 0
• Divide 1420 by 2: 1420 ÷ 2 : Remainder = 0
• Divide 1420 by 4: 1420 ÷ 4 : Remainder = 0
• Divide 1420 by 5: 1420 ÷ 5 : Remainder = 0
• Divide 1420 by 10: 1420 ÷ 10 : Remainder = 0
• Divide 1420 by 20: 1420 ÷ 20 : Remainder = 0
• Divide 1420 by 71: 1420 ÷ 71 : Remainder = 0
• Divide 1420 by 142: 1420 ÷ 142 : Remainder = 0
• Divide 1420 by 284: 1420 ÷ 284 : Remainder = 0
• Divide 1420 by 355: 1420 ÷ 355 : Remainder = 0
• Divide 1420 by 710: 1420 ÷ 710 : Remainder = 0
• Divide 1420 by 1420: 1420 ÷ 1420 : Remainder = 0

Hence, Factors of 1420 are 1, 2, 4, 5, 10, 20, 71, 142, 284, 355, 710, and 1420

#### 2. Steps to find factors of 1420 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 1420 using the division method, follow these steps:

• Step 1. Start dividing 1420 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 1420, which is 2. Divide 1420 by 2 to obtain the quotient (710).
1420 ÷ 2 = 710
• Step 3. Repeat step 1 with the obtained quotient (710).
710 ÷ 2 = 355
355 ÷ 5 = 71
71 ÷ 71 = 1

So, the prime factorization of 1420 is, 1420 = 2 x 2 x 5 x 71.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1420 as shown below:

So, the prime factorization of 1420 is, 1420 = 2 x 2 x 5 x 71.

#### 3. Find factors of 1420 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 1420 would be the two numbers which, when multiplied, give 1420 as the result.

The following table represents the calculation of factors of 1420 in pairs:

Factor Pair Pair Factorization
1 and 1420 1 x 1420 = 1420
2 and 710 2 x 710 = 1420
4 and 355 4 x 355 = 1420
5 and 284 5 x 284 = 1420
10 and 142 10 x 142 = 1420
20 and 71 20 x 71 = 1420

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 1420. They are called negative pair factors.

Hence, the negative pairs of 1420 would be ( -1 , -1420 ) , ( -2 , -710 ) , ( -4 , -355 ) , ( -5 , -284 ) , ( -10 , -142 ) and ( -20 , -71 ) .

#### What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 1420 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 1420.
• Every number is a factor of zero (0), since 1420 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 4, 5, 10, 20, 71, 142, 284, 355, 710, 1420 are exact divisors of 1420.
• Factors of 1420 are 1, 2, 4, 5, 10, 20, 71, 142, 284, 355, 710, 1420. Each factor divides 1420 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 5, 10, 20, 71, 142, 284, 355, 710, 1420 are all less than or equal to 1420.

• Which is the smallest prime factor of 1420?

The smallest prime factor of 1420 is 2.

• Is 1420 a whole number?

Yes 1420 is a whole number.

• What are the prime factors of 1420?

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

• What two numbers make 1420?

Two numbers that make 1420 are 2 and 710.

• What are multiples of 1420?

First five multiples of 1420 are 2840, 4260, 5680, 7100.

• What is the sum of all factors of 1420?

The sum of all factors of 1420 is 3024.

• What are five multiples of 1420?

First five multiples of 1420 are 2840, 4260, 5680, 7100, 8520.

• Is 1420 a perfect square?

No 1420 is not a perfect square.

• What is the greatest prime factors of 1420?

The greatest prime factor of 1420 is 71.

#### Examples of Factors

How many factors are there for 1420?

Factors of 1420 are 1, 2, 4, 5, 10, 20, 71, 142, 284, 355, 710, 1420.
So there are in total 12 factors.

Kevin has been asked to write 11 factor(s) of 1420. Can you predict the answer?

11 factor(s) of 1420 are 1, 2, 4, 5, 10, 20, 71, 142, 284, 355, 710.

Sammy is puzzled while calculating the prime factors of 1420. Can you help him find them?

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

What is prime factorization of 1420?

Prime factorization of 1420 is 2 x 2 x 5 x 71 = 22 x 5 x 71.

Ariel has been assigned the task to find the product of all the prime factors of 1420. Can you help her?

Prime factors of 1420 are 2, 2, 5, 71.
Hence, the product of prime factors of 710.

Can you help Rubel to find out the product of the even factors of 1420?

Factors of 1420 are 1, 2, 4, 5, 10, 20, 71, 142, 284, 355, 710, 1420.
Even factors of 1420 are 2, 4, 10, 20, 142, 284, 710, 1420.
Hence, product of even factors of 1420 is; 2 x 4 x 10 x 20 x 142 x 284 x 710 x 1420 = 65053903360000.

Joy wants to calculate mean of all the factors of 1420. Help him in finding the mean of 1420.

Factors of 1420 are 1, 2, 4, 5, 10, 20, 71, 142, 284, 355, 710, 1420.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 1420 is 1 + 2 + 4 + 5 + 10 + 20 + 71 + 142 + 284 + 355 + 710 + 1420 = 3024.
Hence, the mean of factors of 1420 is 3024 ÷ 12 = 252.00.