# Factors of 3402

Factors of 3402 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 81, 126, 162, 189, 243, 378, 486, 567, 1134, 1701, and 3402

#### How to find factors of a number

 1.   Find factors of 3402 using Division Method 2.   Find factors of 3402 using Prime Factorization 3.   Find factors of 3402 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 3402

• Divide 3402 by 1: 3402 ÷ 1 : Remainder = 0
• Divide 3402 by 2: 3402 ÷ 2 : Remainder = 0
• Divide 3402 by 3: 3402 ÷ 3 : Remainder = 0
• Divide 3402 by 6: 3402 ÷ 6 : Remainder = 0
• Divide 3402 by 7: 3402 ÷ 7 : Remainder = 0
• Divide 3402 by 9: 3402 ÷ 9 : Remainder = 0
• Divide 3402 by 14: 3402 ÷ 14 : Remainder = 0
• Divide 3402 by 18: 3402 ÷ 18 : Remainder = 0
• Divide 3402 by 21: 3402 ÷ 21 : Remainder = 0
• Divide 3402 by 27: 3402 ÷ 27 : Remainder = 0
• Divide 3402 by 42: 3402 ÷ 42 : Remainder = 0
• Divide 3402 by 54: 3402 ÷ 54 : Remainder = 0
• Divide 3402 by 63: 3402 ÷ 63 : Remainder = 0
• Divide 3402 by 81: 3402 ÷ 81 : Remainder = 0
• Divide 3402 by 126: 3402 ÷ 126 : Remainder = 0
• Divide 3402 by 162: 3402 ÷ 162 : Remainder = 0
• Divide 3402 by 189: 3402 ÷ 189 : Remainder = 0
• Divide 3402 by 243: 3402 ÷ 243 : Remainder = 0
• Divide 3402 by 378: 3402 ÷ 378 : Remainder = 0
• Divide 3402 by 486: 3402 ÷ 486 : Remainder = 0
• Divide 3402 by 567: 3402 ÷ 567 : Remainder = 0
• Divide 3402 by 1134: 3402 ÷ 1134 : Remainder = 0
• Divide 3402 by 1701: 3402 ÷ 1701 : Remainder = 0
• Divide 3402 by 3402: 3402 ÷ 3402 : Remainder = 0

Hence, Factors of 3402 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 81, 126, 162, 189, 243, 378, 486, 567, 1134, 1701, and 3402

#### 2. Steps to find factors of 3402 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 3402 using the division method, follow these steps:

• Step 1. Start dividing 3402 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 3402, which is 2. Divide 3402 by 2 to obtain the quotient (1701).
3402 ÷ 2 = 1701
• Step 3. Repeat step 1 with the obtained quotient (1701).
1701 ÷ 3 = 567
567 ÷ 3 = 189
189 ÷ 3 = 63
63 ÷ 3 = 21
21 ÷ 3 = 7
7 ÷ 7 = 1

So, the prime factorization of 3402 is, 3402 = 2 x 3 x 3 x 3 x 3 x 3 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 3402 as shown below:

So, the prime factorization of 3402 is, 3402 = 2 x 3 x 3 x 3 x 3 x 3 x 7.

#### 3. Find factors of 3402 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 3402 would be the two numbers which, when multiplied, give 3402 as the result.

The following table represents the calculation of factors of 3402 in pairs:

Factor Pair Pair Factorization
1 and 3402 1 x 3402 = 3402
2 and 1701 2 x 1701 = 3402
3 and 1134 3 x 1134 = 3402
6 and 567 6 x 567 = 3402
7 and 486 7 x 486 = 3402
9 and 378 9 x 378 = 3402
14 and 243 14 x 243 = 3402
18 and 189 18 x 189 = 3402
21 and 162 21 x 162 = 3402
27 and 126 27 x 126 = 3402
42 and 81 42 x 81 = 3402
54 and 63 54 x 63 = 3402

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 3402. They are called negative pair factors.

Hence, the negative pairs of 3402 would be ( -1 , -3402 ) , ( -2 , -1701 ) , ( -3 , -1134 ) , ( -6 , -567 ) , ( -7 , -486 ) , ( -9 , -378 ) , ( -14 , -243 ) , ( -18 , -189 ) , ( -21 , -162 ) , ( -27 , -126 ) , ( -42 , -81 ) and ( -54 , -63 ) .

#### How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 3402 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, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 81, 126, 162, 189, 243, 378, 486, 567, 1134, 1701, 3402 are exact divisors of 3402.
• 1 is a factor of every number. Eg. 1 is a factor of 3402.
• Every number is a factor of zero (0), since 3402 x 0 = 0.

• Which is the smallest prime factor of 3402?

Smallest prime factor of 3402 is 2.

• Is 3402 a perfect square?

No 3402 is not a perfect square.

• What are five multiples of 3402?

First five multiples of 3402 are 6804, 10206, 13608, 17010, 20412.

• What is prime factorization of 3402?

Prime factorization of 3402 is 2 x 3 x 3 x 3 x 3 x 3 x 7.

• What are factors of 3402?

Factors of 3402 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 81, 126, 162, 189, 243, 378, 486, 567, 1134, 1701, 3402.

• How do you find factors of a negative number? ( eg. -3402 )?

Factors of -3402 are -1, -2, -3, -6, -7, -9, -14, -18, -21, -27, -42, -54, -63, -81, -126, -162, -189, -243, -378, -486, -567, -1134, -1701, -3402.

• Is 3402 a whole number?

Yes 3402 is a whole number.

• Which is greatest factor of 3402?

The greatest factor of 3402 is 1701.

• What are the prime factors of 3402?

The factors of 3402 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 81, 126, 162, 189, 243, 378, 486, 567, 1134, 1701, 3402.
Prime factors of 3402 are 2, 3, 3, 3, 3, 3, 7.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 3402. Can you help her?

Prime factors of 3402 are 2, 3, 3, 3, 3, 3, 7.
Hence, the product of prime factors of 42.

Can you help Rubel to find out the product of the even factors of 3402?

Factors of 3402 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 81, 126, 162, 189, 243, 378, 486, 567, 1134, 1701, 3402.
Even factors of 3402 are 2, 6, 14, 18, 42, 54, 126, 162, 378, 486, 1134, 3402.
Hence, product of even factors of 3402 is; 2 x 6 x 14 x 18 x 42 x 54 x 126 x 162 x 378 x 486 x 1134 x 3402 = 9.921694023599456e+22.

Joy wants to calculate mean of all the factors of 3402. Help him in finding the mean of 3402.

Factors of 3402 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 81, 126, 162, 189, 243, 378, 486, 567, 1134, 1701, 3402.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 3402 is 1 + 2 + 3 + 6 + 7 + 9 + 14 + 18 + 21 + 27 + 42 + 54 + 63 + 81 + 126 + 162 + 189 + 243 + 378 + 486 + 567 + 1134 + 1701 + 3402 = 8736.
Hence, the mean of factors of 3402 is 8736 ÷ 24 = 364.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 3402? Help her in writing all the factors.

Positive factors are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 81, 126, 162, 189, 243, 378, 486, 567, 1134, 1701, 3402.
Negative factors are -1, -2, -3, -6, -7, -9, -14, -18, -21, -27, -42, -54, -63, -81, -126, -162, -189, -243, -378, -486, -567, -1134, -1701, -3402.

How many factors are there for 3402?

Factors of 3402 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 81, 126, 162, 189, 243, 378, 486, 567, 1134, 1701, 3402.
So there are in total 24 factors.

Joey wants to write all the prime factors of 3402 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 3402 are 2, 3, 3, 3, 3, 3, 7.
So in exponential form it can be written as 2 x 35 x 7.

Kevin has been asked to write 23 factor(s) of 3402. Can you predict the answer?

23 factor(s) of 3402 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 81, 126, 162, 189, 243, 378, 486, 567, 1134, 1701.