# Factors of 354

Factors of 354 are 1, 2, 3, 6, 59, 118, 177, and 354

#### How to find factors of a number

 1.   Find factors of 354 using Division Method 2.   Find factors of 354 using Prime Factorization 3.   Find factors of 354 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 354

• Divide 354 by 1: 354 ÷ 1 : Remainder = 0
• Divide 354 by 2: 354 ÷ 2 : Remainder = 0
• Divide 354 by 3: 354 ÷ 3 : Remainder = 0
• Divide 354 by 6: 354 ÷ 6 : Remainder = 0
• Divide 354 by 59: 354 ÷ 59 : Remainder = 0
• Divide 354 by 118: 354 ÷ 118 : Remainder = 0
• Divide 354 by 177: 354 ÷ 177 : Remainder = 0
• Divide 354 by 354: 354 ÷ 354 : Remainder = 0

Hence, Factors of 354 are 1, 2, 3, 6, 59, 118, 177, and 354

#### 2. Steps to find factors of 354 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 354 using the division method, follow these steps:

• Step 1. Start dividing 354 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 354, which is 2. Divide 354 by 2 to obtain the quotient (177).
354 ÷ 2 = 177
• Step 3. Repeat step 1 with the obtained quotient (177).
177 ÷ 3 = 59
59 ÷ 59 = 1

So, the prime factorization of 354 is, 354 = 2 x 3 x 59.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 354 as shown below:

So, the prime factorization of 354 is, 354 = 2 x 3 x 59.

#### 3. Find factors of 354 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 354 would be the two numbers which, when multiplied, give 354 as the result.

The following table represents the calculation of factors of 354 in pairs:

Factor Pair Pair Factorization
1 and 354 1 x 354 = 354
2 and 177 2 x 177 = 354
3 and 118 3 x 118 = 354
6 and 59 6 x 59 = 354

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 354. They are called negative pair factors.

Hence, the negative pairs of 354 would be ( -1 , -354 ) , ( -2 , -177 ) , ( -3 , -118 ) and ( -6 , -59 ) .

#### 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. 354 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, 59, 118, 177, 354 are exact divisors of 354.
• 1 is a factor of every number. Eg. 1 is a factor of 354.
• Every number is a factor of zero (0), since 354 x 0 = 0.

• What are the prime factors of 354?

The factors of 354 are 1, 2, 3, 6, 59, 118, 177, 354.
Prime factors of 354 are 2, 3, 59.

• What two numbers make 354?

Two numbers that make 354 are 2 and 177.

• What is the greatest prime factors of 354?

The greatest prime factor of 354 is 59.

• What are factors of 354?

Factors of 354 are 1, 2, 3, 6, 59, 118, 177, 354.

• How do you find factors of a negative number? ( eg. -354 )?

Factors of -354 are -1, -2, -3, -6, -59, -118, -177, -354.

• What are five multiples of 354?

First five multiples of 354 are 708, 1062, 1416, 1770, 2124.

• Write some multiples of 354?

First five multiples of 354 are 708, 1062, 1416, 1770.

• Is 354 a perfect square?

No 354 is not a perfect square.

• What two numbers make 354?

Two numbers that make 354 are 2 and 177.

#### Examples of Factors

What is prime factorization of 354?

Prime factorization of 354 is 2 x 3 x 59 = 2 x 3 x 59.

Sammy is puzzled while calculating the prime factors of 354. Can you help him find them?

Factors of 354 are 1, 2, 3, 6, 59, 118, 177, 354.
Prime factors of 354 are 2, 3, 59

Kevin has been asked to write 7 factor(s) of 354. Can you predict the answer?

7 factor(s) of 354 are 1, 2, 3, 6, 59, 118, 177.

Joey wants to write all the prime factors of 354 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 354 are 2, 3, 59.
So in exponential form it can be written as 2 x 3 x 59.

How many factors are there for 354?

Factors of 354 are 1, 2, 3, 6, 59, 118, 177, 354.
So there are in total 8 factors.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 354? Help her in writing all the factors.

Positive factors are 1, 2, 3, 6, 59, 118, 177, 354.
Negative factors are -1, -2, -3, -6, -59, -118, -177, -354.

Can you help Rubel to find out the product of the even factors of 354?

Factors of 354 are 1, 2, 3, 6, 59, 118, 177, 354.
Even factors of 354 are 2, 6, 118, 354.
Hence, product of even factors of 354 is; 2 x 6 x 118 x 354 = 501264.