# Factors of 1710

Factors of 1710 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 19, 30, 38, 45, 57, 90, 95, 114, 171, 190, 285, 342, 570, 855, and 1710

#### How to find factors of a number

 1.   Find factors of 1710 using Division Method 2.   Find factors of 1710 using Prime Factorization 3.   Find factors of 1710 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 1710

• Divide 1710 by 1: 1710 ÷ 1 : Remainder = 0
• Divide 1710 by 2: 1710 ÷ 2 : Remainder = 0
• Divide 1710 by 3: 1710 ÷ 3 : Remainder = 0
• Divide 1710 by 5: 1710 ÷ 5 : Remainder = 0
• Divide 1710 by 6: 1710 ÷ 6 : Remainder = 0
• Divide 1710 by 9: 1710 ÷ 9 : Remainder = 0
• Divide 1710 by 10: 1710 ÷ 10 : Remainder = 0
• Divide 1710 by 15: 1710 ÷ 15 : Remainder = 0
• Divide 1710 by 18: 1710 ÷ 18 : Remainder = 0
• Divide 1710 by 19: 1710 ÷ 19 : Remainder = 0
• Divide 1710 by 30: 1710 ÷ 30 : Remainder = 0
• Divide 1710 by 38: 1710 ÷ 38 : Remainder = 0
• Divide 1710 by 45: 1710 ÷ 45 : Remainder = 0
• Divide 1710 by 57: 1710 ÷ 57 : Remainder = 0
• Divide 1710 by 90: 1710 ÷ 90 : Remainder = 0
• Divide 1710 by 95: 1710 ÷ 95 : Remainder = 0
• Divide 1710 by 114: 1710 ÷ 114 : Remainder = 0
• Divide 1710 by 171: 1710 ÷ 171 : Remainder = 0
• Divide 1710 by 190: 1710 ÷ 190 : Remainder = 0
• Divide 1710 by 285: 1710 ÷ 285 : Remainder = 0
• Divide 1710 by 342: 1710 ÷ 342 : Remainder = 0
• Divide 1710 by 570: 1710 ÷ 570 : Remainder = 0
• Divide 1710 by 855: 1710 ÷ 855 : Remainder = 0
• Divide 1710 by 1710: 1710 ÷ 1710 : Remainder = 0

Hence, Factors of 1710 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 19, 30, 38, 45, 57, 90, 95, 114, 171, 190, 285, 342, 570, 855, and 1710

#### 2. Steps to find factors of 1710 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 1710 using the division method, follow these steps:

• Step 1. Start dividing 1710 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 1710, which is 2. Divide 1710 by 2 to obtain the quotient (855).
1710 ÷ 2 = 855
• Step 3. Repeat step 1 with the obtained quotient (855).
855 ÷ 3 = 285
285 ÷ 3 = 95
95 ÷ 5 = 19
19 ÷ 19 = 1

So, the prime factorization of 1710 is, 1710 = 2 x 3 x 3 x 5 x 19.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1710 as shown below:

So, the prime factorization of 1710 is, 1710 = 2 x 3 x 3 x 5 x 19.

#### 3. Find factors of 1710 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 1710 would be the two numbers which, when multiplied, give 1710 as the result.

The following table represents the calculation of factors of 1710 in pairs:

Factor Pair Pair Factorization
1 and 1710 1 x 1710 = 1710
2 and 855 2 x 855 = 1710
3 and 570 3 x 570 = 1710
5 and 342 5 x 342 = 1710
6 and 285 6 x 285 = 1710
9 and 190 9 x 190 = 1710
10 and 171 10 x 171 = 1710
15 and 114 15 x 114 = 1710
18 and 95 18 x 95 = 1710
19 and 90 19 x 90 = 1710
30 and 57 30 x 57 = 1710
38 and 45 38 x 45 = 1710

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 1710. They are called negative pair factors.

Hence, the negative pairs of 1710 would be ( -1 , -1710 ) , ( -2 , -855 ) , ( -3 , -570 ) , ( -5 , -342 ) , ( -6 , -285 ) , ( -9 , -190 ) , ( -10 , -171 ) , ( -15 , -114 ) , ( -18 , -95 ) , ( -19 , -90 ) , ( -30 , -57 ) and ( -38 , -45 ) .

#### 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. 1710 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, 3, 5, 6, 9, 10, 15, 18, 19, 30, 38, 45, 57, 90, 95, 114, 171, 190, 285, 342, 570, 855, 1710 are exact divisors of 1710.
• 1 is a factor of every number. Eg. 1 is a factor of 1710.
• Every number is a factor of zero (0), since 1710 x 0 = 0.

• Which is the smallest prime factor of 1710?

Smallest prime factor of 1710 is 2.

• Is 1710 a perfect square?

No 1710 is not a perfect square.

• What are five multiples of 1710?

First five multiples of 1710 are 3420, 5130, 6840, 8550, 10260.

• What is prime factorization of 1710?

Prime factorization of 1710 is 2 x 3 x 3 x 5 x 19.

• What are factors of 1710?

Factors of 1710 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 19, 30, 38, 45, 57, 90, 95, 114, 171, 190, 285, 342, 570, 855, 1710.

• How do you find factors of a negative number? ( eg. -1710 )?

Factors of -1710 are -1, -2, -3, -5, -6, -9, -10, -15, -18, -19, -30, -38, -45, -57, -90, -95, -114, -171, -190, -285, -342, -570, -855, -1710.

• Is 1710 a whole number?

Yes 1710 is a whole number.

• Which is greatest factor of 1710?

The greatest factor of 1710 is 855.

• What are the prime factors of 1710?

The factors of 1710 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 19, 30, 38, 45, 57, 90, 95, 114, 171, 190, 285, 342, 570, 855, 1710.
Prime factors of 1710 are 2, 3, 3, 5, 19.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 1710. Can you help her?

Prime factors of 1710 are 2, 3, 3, 5, 19.
Hence, the product of prime factors of 570.

Can you help Rubel to find out the product of the even factors of 1710?

Factors of 1710 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 19, 30, 38, 45, 57, 90, 95, 114, 171, 190, 285, 342, 570, 855, 1710.
Even factors of 1710 are 2, 6, 10, 18, 30, 38, 90, 114, 190, 342, 570, 1710.
Hence, product of even factors of 1710 is; 2 x 6 x 10 x 18 x 30 x 38 x 90 x 114 x 190 x 342 x 570 x 1710 = 1.600135042849344e+21.

Joy wants to calculate mean of all the factors of 1710. Help him in finding the mean of 1710.

Factors of 1710 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 19, 30, 38, 45, 57, 90, 95, 114, 171, 190, 285, 342, 570, 855, 1710.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 1710 is 1 + 2 + 3 + 5 + 6 + 9 + 10 + 15 + 18 + 19 + 30 + 38 + 45 + 57 + 90 + 95 + 114 + 171 + 190 + 285 + 342 + 570 + 855 + 1710 = 4680.
Hence, the mean of factors of 1710 is 4680 ÷ 24 = 195.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 1710? Help her in writing all the factors.

Positive factors are 1, 2, 3, 5, 6, 9, 10, 15, 18, 19, 30, 38, 45, 57, 90, 95, 114, 171, 190, 285, 342, 570, 855, 1710.
Negative factors are -1, -2, -3, -5, -6, -9, -10, -15, -18, -19, -30, -38, -45, -57, -90, -95, -114, -171, -190, -285, -342, -570, -855, -1710.

How many factors are there for 1710?

Factors of 1710 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 19, 30, 38, 45, 57, 90, 95, 114, 171, 190, 285, 342, 570, 855, 1710.
So there are in total 24 factors.

Joey wants to write all the prime factors of 1710 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1710 are 2, 3, 3, 5, 19.
So in exponential form it can be written as 2 x 32 x 5 x 19.

Kevin has been asked to write 23 factor(s) of 1710. Can you predict the answer?

23 factor(s) of 1710 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 19, 30, 38, 45, 57, 90, 95, 114, 171, 190, 285, 342, 570, 855.