1. Steps to find factors of 412 using Division Method

Example: Find factors of 412

  • Divide 412 by 1: 412 ÷ 1 : Remainder = 0
  • Divide 412 by 2: 412 ÷ 2 : Remainder = 0
  • Divide 412 by 4: 412 ÷ 4 : Remainder = 0
  • Divide 412 by 103: 412 ÷ 103 : Remainder = 0
  • Divide 412 by 206: 412 ÷ 206 : Remainder = 0
  • Divide 412 by 412: 412 ÷ 412 : Remainder = 0

Hence, Factors of 412 are 1, 2, 4, 103, 206, and 412

2. Steps to find factors of 412 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 412 using the division method, follow these steps:

  • Step 1. Start dividing 412 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 412, which is 2. Divide 412 by 2 to obtain the quotient (206).
    412 ÷ 2 = 206
  • Step 3. Repeat step 1 with the obtained quotient (206).
    206 ÷ 2 = 103
    103 ÷ 103 = 1

So, the prime factorization of 412 is, 412 = 2 x 2 x 103.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 412 as shown below:

So, the prime factorization of 412 is, 412 = 2 x 2 x 103.

3. Find factors of 412 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 412 would be the two numbers which, when multiplied, give 412 as the result.

The following table represents the calculation of factors of 412 in pairs:

Factor Pair Pair Factorization
1 and 412 1 x 412 = 412
2 and 206 2 x 206 = 412
4 and 103 4 x 103 = 412

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 412. They are called negative pair factors.

Hence, the negative pairs of 412 would be ( -1 , -412 ) , ( -2 , -206 ) and ( -4 , -103 ) .

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. 412 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 412.
  • Every number is a factor of zero (0), since 412 x 0 = 0.
  • 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, 4, 103, 206, 412 are exact divisors of 412.
  • Factors of 412 are 1, 2, 4, 103, 206, 412. Each factor divides 412 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 103, 206, 412 are all less than or equal to 412.

Frequently Asked Questions

  • Which is the smallest prime factor of 412?

    The smallest prime factor of 412 is 2.

  • Is 412 a whole number?

    Yes 412 is a whole number.

  • What are the prime factors of 412?

    The factors of 412 are 1, 2, 4, 103, 206, 412.
    Prime factors of 412 are 2, 2, 103.

  • What two numbers make 412?

    Two numbers that make 412 are 2 and 206.

  • What are multiples of 412?

    First five multiples of 412 are 824, 1236, 1648, 2060.

  • What is the sum of all factors of 412?

    The sum of all factors of 412 is 728.

  • What are five multiples of 412?

    First five multiples of 412 are 824, 1236, 1648, 2060, 2472.

  • Is 412 a perfect square?

    No 412 is not a perfect square.

  • What is the greatest prime factors of 412?

    The greatest prime factor of 412 is 103.

Examples of Factors

How many factors are there for 412?

Factors of 412 are 1, 2, 4, 103, 206, 412.
So there are in total 6 factors.

Kevin has been asked to write 5 factor(s) of 412. Can you predict the answer?

5 factor(s) of 412 are 1, 2, 4, 103, 206.

Sammy is puzzled while calculating the prime factors of 412. Can you help him find them?

Factors of 412 are 1, 2, 4, 103, 206, 412.
Prime factors of 412 are 2, 2, 103

What is prime factorization of 412?

Prime factorization of 412 is 2 x 2 x 103 = 22 x 103.

Ariel has been assigned the task to find the product of all the prime factors of 412. Can you help her?

Prime factors of 412 are 2, 2, 103.
Hence, the product of prime factors of 206.

Can you help Rubel to find out the product of the even factors of 412?

Factors of 412 are 1, 2, 4, 103, 206, 412.
Even factors of 412 are 2, 4, 206, 412.
Hence, product of even factors of 412 is; 2 x 4 x 206 x 412 = 678976.

Joy wants to calculate mean of all the factors of 412. Help him in finding the mean of 412.

Factors of 412 are 1, 2, 4, 103, 206, 412.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 412 is 1 + 2 + 4 + 103 + 206 + 412 = 728.
Hence, the mean of factors of 412 is 728 ÷ 6 = 121.33.