1. Steps to find factors of 402 using Division Method

Example: Find factors of 402

  • Divide 402 by 1: 402 ÷ 1 : Remainder = 0
  • Divide 402 by 2: 402 ÷ 2 : Remainder = 0
  • Divide 402 by 3: 402 ÷ 3 : Remainder = 0
  • Divide 402 by 6: 402 ÷ 6 : Remainder = 0
  • Divide 402 by 67: 402 ÷ 67 : Remainder = 0
  • Divide 402 by 134: 402 ÷ 134 : Remainder = 0
  • Divide 402 by 201: 402 ÷ 201 : Remainder = 0
  • Divide 402 by 402: 402 ÷ 402 : Remainder = 0

Hence, Factors of 402 are 1, 2, 3, 6, 67, 134, 201, and 402

2. Steps to find factors of 402 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 402 using the division method, follow these steps:

  • Step 1. Start dividing 402 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 402, which is 2. Divide 402 by 2 to obtain the quotient (201).
    402 ÷ 2 = 201
  • Step 3. Repeat step 1 with the obtained quotient (201).
    201 ÷ 3 = 67
    67 ÷ 67 = 1

So, the prime factorization of 402 is, 402 = 2 x 3 x 67.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 402 as shown below:

So, the prime factorization of 402 is, 402 = 2 x 3 x 67.

3. Find factors of 402 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 402 would be the two numbers which, when multiplied, give 402 as the result.

The following table represents the calculation of factors of 402 in pairs:

Factor Pair Pair Factorization
1 and 402 1 x 402 = 402
2 and 201 2 x 201 = 402
3 and 134 3 x 134 = 402
6 and 67 6 x 67 = 402

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 402. They are called negative pair factors.

Hence, the negative pairs of 402 would be ( -1 , -402 ) , ( -2 , -201 ) , ( -3 , -134 ) and ( -6 , -67 ) .

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. 402 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, 67, 134, 201, 402 are exact divisors of 402.
  • 1 is a factor of every number. Eg. 1 is a factor of 402.
  • Every number is a factor of zero (0), since 402 x 0 = 0.

Frequently Asked Questions

  • How do you find factors of a negative number? ( eg. -402 )?

    Factors of -402 are -1, -2, -3, -6, -67, -134, -201, -402.

  • What is the sum of all factors of 402?

    The sum of all factors of 402 is 816.

  • What is prime factorization of 402?

    Prime factorization of 402 is 2 x 3 x 67.

  • What are the pair factors of 402?

    Pair factors of 402 are (1,402), (2,201), (3,134), (6,67).

  • What are six multiples of 402?

    First five multiples of 402 are 804, 1206, 1608, 2010, 2412, 2814.

  • Is 402 a whole number?

    Yes 402 is a whole number.

  • Which is the smallest prime factor of 402?

    Smallest prime factor of 402 is 2.

  • What are five multiples of 402?

    First five multiples of 402 are 804, 1206, 1608, 2010, 2412.

  • Write all factors of 402?

    Factors of 402 are 1, 2, 3, 6, 67, 134, 201, 402.

Examples of Factors

Joey wants to write all the prime factors of 402 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 402 are 2, 3, 67.
So in exponential form it can be written as 2 x 3 x 67.

How many factors are there for 402?

Factors of 402 are 1, 2, 3, 6, 67, 134, 201, 402.
So there are in total 8 factors.

Kevin has been asked to write 7 factor(s) of 402. Can you predict the answer?

7 factor(s) of 402 are 1, 2, 3, 6, 67, 134, 201.

Sammy is puzzled while calculating the prime factors of 402. Can you help him find them?

Factors of 402 are 1, 2, 3, 6, 67, 134, 201, 402.
Prime factors of 402 are 2, 3, 67

What is prime factorization of 402?

Prime factorization of 402 is 2 x 3 x 67 = 2 x 3 x 67.

Ariel has been assigned the task to find the product of all the prime factors of 402. Can you help her?

Prime factors of 402 are 2, 3, 67.
Hence, the product of prime factors of 402.

Can you help Rubel to find out the product of the even factors of 402?

Factors of 402 are 1, 2, 3, 6, 67, 134, 201, 402.
Even factors of 402 are 2, 6, 134, 402.
Hence, product of even factors of 402 is; 2 x 6 x 134 x 402 = 646416.