# Factors of 1210

Factors of 1210 are 1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605, and 1210

#### How to find factors of a number

 1.   Find factors of 1210 using Division Method 2.   Find factors of 1210 using Prime Factorization 3.   Find factors of 1210 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 1210

• Divide 1210 by 1: 1210 ÷ 1 : Remainder = 0
• Divide 1210 by 2: 1210 ÷ 2 : Remainder = 0
• Divide 1210 by 5: 1210 ÷ 5 : Remainder = 0
• Divide 1210 by 10: 1210 ÷ 10 : Remainder = 0
• Divide 1210 by 11: 1210 ÷ 11 : Remainder = 0
• Divide 1210 by 22: 1210 ÷ 22 : Remainder = 0
• Divide 1210 by 55: 1210 ÷ 55 : Remainder = 0
• Divide 1210 by 110: 1210 ÷ 110 : Remainder = 0
• Divide 1210 by 121: 1210 ÷ 121 : Remainder = 0
• Divide 1210 by 242: 1210 ÷ 242 : Remainder = 0
• Divide 1210 by 605: 1210 ÷ 605 : Remainder = 0
• Divide 1210 by 1210: 1210 ÷ 1210 : Remainder = 0

Hence, Factors of 1210 are 1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605, and 1210

#### 2. Steps to find factors of 1210 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 1210 using the division method, follow these steps:

• Step 1. Start dividing 1210 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 1210, which is 2. Divide 1210 by 2 to obtain the quotient (605).
1210 ÷ 2 = 605
• Step 3. Repeat step 1 with the obtained quotient (605).
605 ÷ 5 = 121
121 ÷ 11 = 11
11 ÷ 11 = 1

So, the prime factorization of 1210 is, 1210 = 2 x 5 x 11 x 11.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1210 as shown below:

So, the prime factorization of 1210 is, 1210 = 2 x 5 x 11 x 11.

#### 3. Find factors of 1210 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 1210 would be the two numbers which, when multiplied, give 1210 as the result.

The following table represents the calculation of factors of 1210 in pairs:

Factor Pair Pair Factorization
1 and 1210 1 x 1210 = 1210
2 and 605 2 x 605 = 1210
5 and 242 5 x 242 = 1210
10 and 121 10 x 121 = 1210
11 and 110 11 x 110 = 1210
22 and 55 22 x 55 = 1210

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 1210. They are called negative pair factors.

Hence, the negative pairs of 1210 would be ( -1 , -1210 ) , ( -2 , -605 ) , ( -5 , -242 ) , ( -10 , -121 ) , ( -11 , -110 ) and ( -22 , -55 ) .

#### 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. 1210 is a factor of itself.
• 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, 5, 10, 11, 22, 55, 110, 121, 242, 605, 1210 are exact divisors of 1210.
• 1 is a factor of every number. Eg. 1 is a factor of 1210.
• Every number is a factor of zero (0), since 1210 x 0 = 0.

• Is 1210 a perfect square?

No 1210 is not a perfect square.

• What are factors of 1210?

Factors of 1210 are 1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605, 1210.

• Which is greatest factor of 1210?

The greatest factor of 1210 is 605.

• What is the sum of all factors of 1210?

The sum of all factors of 1210 is 2394.

• What are multiples of 1210?

First five multiples of 1210 are 2420, 3630, 4840, 6050.

• What is the greatest prime factors of 1210?

The greatest prime factor of 1210 is 11.

• What are six multiples of 1210?

First five multiples of 1210 are 2420, 3630, 4840, 6050, 7260, 8470.

• What is prime factorization of 1210?

Prime factorization of 1210 is 2 x 5 x 11 x 11.

• Is 1210 a whole number?

Yes 1210 is a whole number.

#### Examples of Factors

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 1210? Help her in writing all the factors.

Positive factors are 1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605, 1210.
Negative factors are -1, -2, -5, -10, -11, -22, -55, -110, -121, -242, -605, -1210.

Can you help Sammy find out the product of the odd factors of 1210?

Factors of 1210 are 1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605, 1210.
Odd factors of 1210 are 1, 5, 11, 55, 121, 605.
Hence product of odd factors of 1210 is; 1 x 5 x 11 x 55 x 121 x 605 = 221445125.

Joey wants to write all the prime factors of 1210 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1210 are 2, 5, 11, 11.
So in exponential form it can be written as 2 x 5 x 112.

How many factors are there for 1210?

Factors of 1210 are 1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605, 1210.
So there are in total 12 factors.

Kevin has been asked to write 11 factor(s) of 1210. Can you predict the answer?

11 factor(s) of 1210 are 1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605.

Sammy is puzzled while calculating the prime factors of 1210. Can you help him find them?

Factors of 1210 are 1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605, 1210.
Prime factors of 1210 are 2, 5, 11, 11

What is prime factorization of 1210?

Prime factorization of 1210 is 2 x 5 x 11 x 11 = 2 x 5 x 112.