1. Steps to find factors of 414 using Division Method

Example: Find factors of 414

  • Divide 414 by 1: 414 ÷ 1 : Remainder = 0
  • Divide 414 by 2: 414 ÷ 2 : Remainder = 0
  • Divide 414 by 3: 414 ÷ 3 : Remainder = 0
  • Divide 414 by 6: 414 ÷ 6 : Remainder = 0
  • Divide 414 by 9: 414 ÷ 9 : Remainder = 0
  • Divide 414 by 18: 414 ÷ 18 : Remainder = 0
  • Divide 414 by 23: 414 ÷ 23 : Remainder = 0
  • Divide 414 by 46: 414 ÷ 46 : Remainder = 0
  • Divide 414 by 69: 414 ÷ 69 : Remainder = 0
  • Divide 414 by 138: 414 ÷ 138 : Remainder = 0
  • Divide 414 by 207: 414 ÷ 207 : Remainder = 0
  • Divide 414 by 414: 414 ÷ 414 : Remainder = 0

Hence, Factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, and 414

2. Steps to find factors of 414 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 414 using the division method, follow these steps:

  • Step 1. Start dividing 414 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 414, which is 2. Divide 414 by 2 to obtain the quotient (207).
    414 ÷ 2 = 207
  • Step 3. Repeat step 1 with the obtained quotient (207).
    207 ÷ 3 = 69
    69 ÷ 3 = 23
    23 ÷ 23 = 1

So, the prime factorization of 414 is, 414 = 2 x 3 x 3 x 23.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 414 as shown below:

So, the prime factorization of 414 is, 414 = 2 x 3 x 3 x 23.

3. Find factors of 414 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 414 would be the two numbers which, when multiplied, give 414 as the result.

The following table represents the calculation of factors of 414 in pairs:

Factor Pair Pair Factorization
1 and 414 1 x 414 = 414
2 and 207 2 x 207 = 414
3 and 138 3 x 138 = 414
6 and 69 6 x 69 = 414
9 and 46 9 x 46 = 414
18 and 23 18 x 23 = 414

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 414. They are called negative pair factors.

Hence, the negative pairs of 414 would be ( -1 , -414 ) , ( -2 , -207 ) , ( -3 , -138 ) , ( -6 , -69 ) , ( -9 , -46 ) and ( -18 , -23 ) .

How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

Properties of factors

  • Each number is a factor of itself. Eg. 414 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, 9, 18, 23, 46, 69, 138, 207, 414 are exact divisors of 414.
  • 1 is a factor of every number. Eg. 1 is a factor of 414.
  • Every number is a factor of zero (0), since 414 x 0 = 0.

Frequently Asked Questions

  • Which is the smallest prime factor of 414?

    Smallest prime factor of 414 is 2.

  • Is 414 a perfect square?

    No 414 is not a perfect square.

  • What are five multiples of 414?

    First five multiples of 414 are 828, 1242, 1656, 2070, 2484.

  • What is prime factorization of 414?

    Prime factorization of 414 is 2 x 3 x 3 x 23.

  • What are factors of 414?

    Factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414.

  • How do you find factors of a negative number? ( eg. -414 )?

    Factors of -414 are -1, -2, -3, -6, -9, -18, -23, -46, -69, -138, -207, -414.

  • Is 414 a whole number?

    Yes 414 is a whole number.

  • Which is greatest factor of 414?

    The greatest factor of 414 is 207.

  • What are the prime factors of 414?

    The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414.
    Prime factors of 414 are 2, 3, 3, 23.

Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 414. Can you help her?

Prime factors of 414 are 2, 3, 3, 23.
Hence, the product of prime factors of 138.

Can you help Rubel to find out the product of the even factors of 414?

Factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414.
Even factors of 414 are 2, 6, 18, 46, 138, 414.
Hence, product of even factors of 414 is; 2 x 6 x 18 x 46 x 138 x 414 = 567663552.

Joy wants to calculate mean of all the factors of 414. Help him in finding the mean of 414.

Factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 414 is 1 + 2 + 3 + 6 + 9 + 18 + 23 + 46 + 69 + 138 + 207 + 414 = 936.
Hence, the mean of factors of 414 is 936 ÷ 12 = 78.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 414? Help her in writing all the factors.

Positive factors are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414.
Negative factors are -1, -2, -3, -6, -9, -18, -23, -46, -69, -138, -207, -414.

How many factors are there for 414?

Factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414.
So there are in total 12 factors.

Joey wants to write all the prime factors of 414 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 414 are 2, 3, 3, 23.
So in exponential form it can be written as 2 x 32 x 23.

Kevin has been asked to write 11 factor(s) of 414. Can you predict the answer?

11 factor(s) of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207.