Factors of 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:

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.

Frequently Asked Questions

• 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