1. Steps to find factors of 356 using Division Method

Example: Find factors of 356

  • Divide 356 by 1: 356 ÷ 1 : Remainder = 0
  • Divide 356 by 2: 356 ÷ 2 : Remainder = 0
  • Divide 356 by 4: 356 ÷ 4 : Remainder = 0
  • Divide 356 by 89: 356 ÷ 89 : Remainder = 0
  • Divide 356 by 178: 356 ÷ 178 : Remainder = 0
  • Divide 356 by 356: 356 ÷ 356 : Remainder = 0

Hence, Factors of 356 are 1, 2, 4, 89, 178, and 356

2. Steps to find factors of 356 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 356 using the division method, follow these steps:

  • Step 1. Start dividing 356 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 356, which is 2. Divide 356 by 2 to obtain the quotient (178).
    356 ÷ 2 = 178
  • Step 3. Repeat step 1 with the obtained quotient (178).
    178 ÷ 2 = 89
    89 ÷ 89 = 1

So, the prime factorization of 356 is, 356 = 2 x 2 x 89.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 356 as shown below:

So, the prime factorization of 356 is, 356 = 2 x 2 x 89.

3. Find factors of 356 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 356 would be the two numbers which, when multiplied, give 356 as the result.

The following table represents the calculation of factors of 356 in pairs:

Factor Pair Pair Factorization
1 and 356 1 x 356 = 356
2 and 178 2 x 178 = 356
4 and 89 4 x 89 = 356

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 356. They are called negative pair factors.

Hence, the negative pairs of 356 would be ( -1 , -356 ) , ( -2 , -178 ) and ( -4 , -89 ) .

How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

Properties of factors

  • Each number is a factor of itself. Eg. 356 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 356.
  • Every number is a factor of zero (0), since 356 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, 89, 178, 356 are exact divisors of 356.
  • Factors of 356 are 1, 2, 4, 89, 178, 356. Each factor divides 356 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 89, 178, 356 are all less than or equal to 356.

Frequently Asked Questions

  • What are the pair factors of 356?

    Pair factors of 356 are (1,356), (2,178), (4,89).

  • What are five multiples of 356?

    First five multiples of 356 are 712, 1068, 1424, 1780, 2136.

  • What two numbers make 356?

    Two numbers that make 356 are 2 and 178.

  • What is the sum of all factors of 356?

    The sum of all factors of 356 is 630.

  • What are factors of -356?

    Factors of -356 are -1, -2, -4, -89, -178, -356.

  • What are factors of 356?

    Factors of 356 are 1, 2, 4, 89, 178, 356.

  • Is 356 a perfect square?

    No 356 is not a perfect square.

  • Which is the smallest prime factor of 356?

    Smallest prime factor of 356 is 2.

  • Which is greatest factor of 356?

    The greatest factor of 356 is 178.

Examples of Factors

Can you help Sammy find out the product of the odd factors of 356?

Factors of 356 are 1, 2, 4, 89, 178, 356.
Odd factors of 356 are 1, 89.
Hence product of odd factors of 356 is; 1 x 89 = 89.

Joey wants to write all the prime factors of 356 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 356 are 2, 2, 89.
So in exponential form it can be written as 22 x 89.

How many factors are there for 356?

Factors of 356 are 1, 2, 4, 89, 178, 356.
So there are in total 6 factors.

Kevin has been asked to write 5 factor(s) of 356. Can you predict the answer?

5 factor(s) of 356 are 1, 2, 4, 89, 178.

Sammy is puzzled while calculating the prime factors of 356. Can you help him find them?

Factors of 356 are 1, 2, 4, 89, 178, 356.
Prime factors of 356 are 2, 2, 89

What is prime factorization of 356?

Prime factorization of 356 is 2 x 2 x 89 = 22 x 89.

Can you help Rubel to find out the product of the even factors of 356?

Factors of 356 are 1, 2, 4, 89, 178, 356.
Even factors of 356 are 2, 4, 178, 356.
Hence, product of even factors of 356 is; 2 x 4 x 178 x 356 = 506944.