1. Steps to find factors of 428 using Division Method

Example: Find factors of 428

  • Divide 428 by 1: 428 ÷ 1 : Remainder = 0
  • Divide 428 by 2: 428 ÷ 2 : Remainder = 0
  • Divide 428 by 4: 428 ÷ 4 : Remainder = 0
  • Divide 428 by 107: 428 ÷ 107 : Remainder = 0
  • Divide 428 by 214: 428 ÷ 214 : Remainder = 0
  • Divide 428 by 428: 428 ÷ 428 : Remainder = 0

Hence, Factors of 428 are 1, 2, 4, 107, 214, and 428

2. Steps to find factors of 428 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 428 using the division method, follow these steps:

  • Step 1. Start dividing 428 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 428, which is 2. Divide 428 by 2 to obtain the quotient (214).
    428 ÷ 2 = 214
  • Step 3. Repeat step 1 with the obtained quotient (214).
    214 ÷ 2 = 107
    107 ÷ 107 = 1

So, the prime factorization of 428 is, 428 = 2 x 2 x 107.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 428 as shown below:

So, the prime factorization of 428 is, 428 = 2 x 2 x 107.

3. Find factors of 428 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 428 would be the two numbers which, when multiplied, give 428 as the result.

The following table represents the calculation of factors of 428 in pairs:

Factor Pair Pair Factorization
1 and 428 1 x 428 = 428
2 and 214 2 x 214 = 428
4 and 107 4 x 107 = 428

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 428. They are called negative pair factors.

Hence, the negative pairs of 428 would be ( -1 , -428 ) , ( -2 , -214 ) and ( -4 , -107 ) .

What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

Properties of factors

  • Each number is a factor of itself. Eg. 428 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 428.
  • Every number is a factor of zero (0), since 428 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, 107, 214, 428 are exact divisors of 428.
  • Factors of 428 are 1, 2, 4, 107, 214, 428. Each factor divides 428 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 107, 214, 428 are all less than or equal to 428.

Frequently Asked Questions

  • What are the pair factors of 428?

    Pair factors of 428 are (1,428), (2,214), (4,107).

  • What are five multiples of 428?

    First five multiples of 428 are 856, 1284, 1712, 2140, 2568.

  • What two numbers make 428?

    Two numbers that make 428 are 2 and 214.

  • What is the sum of all factors of 428?

    The sum of all factors of 428 is 756.

  • What are factors of -428?

    Factors of -428 are -1, -2, -4, -107, -214, -428.

  • What are factors of 428?

    Factors of 428 are 1, 2, 4, 107, 214, 428.

  • Is 428 a perfect square?

    No 428 is not a perfect square.

  • Which is the smallest prime factor of 428?

    Smallest prime factor of 428 is 2.

  • Which is greatest factor of 428?

    The greatest factor of 428 is 214.

Examples of Factors

Can you help Sammy find out the product of the odd factors of 428?

Factors of 428 are 1, 2, 4, 107, 214, 428.
Odd factors of 428 are 1, 107.
Hence product of odd factors of 428 is; 1 x 107 = 107.

Joey wants to write all the prime factors of 428 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 428 are 2, 2, 107.
So in exponential form it can be written as 22 x 107.

How many factors are there for 428?

Factors of 428 are 1, 2, 4, 107, 214, 428.
So there are in total 6 factors.

Kevin has been asked to write 5 factor(s) of 428. Can you predict the answer?

5 factor(s) of 428 are 1, 2, 4, 107, 214.

Sammy is puzzled while calculating the prime factors of 428. Can you help him find them?

Factors of 428 are 1, 2, 4, 107, 214, 428.
Prime factors of 428 are 2, 2, 107

What is prime factorization of 428?

Prime factorization of 428 is 2 x 2 x 107 = 22 x 107.

Can you help Rubel to find out the product of the even factors of 428?

Factors of 428 are 1, 2, 4, 107, 214, 428.
Even factors of 428 are 2, 4, 214, 428.
Hence, product of even factors of 428 is; 2 x 4 x 214 x 428 = 732736.