# Factors of 146

Factors of 146 are 1, 2, 73, and 146

#### How to find factors of a number

 1.   Find factors of 146 using Division Method 2.   Find factors of 146 using Prime Factorization 3.   Find factors of 146 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 146

• Divide 146 by 1: 146 ÷ 1 : Remainder = 0
• Divide 146 by 2: 146 ÷ 2 : Remainder = 0
• Divide 146 by 73: 146 ÷ 73 : Remainder = 0
• Divide 146 by 146: 146 ÷ 146 : Remainder = 0

Hence, Factors of 146 are 1, 2, 73, and 146

#### 2. Steps to find factors of 146 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 146 using the division method, follow these steps:

• Step 1. Start dividing 146 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 146, which is 2. Divide 146 by 2 to obtain the quotient (73).
146 ÷ 2 = 73
• Step 3. Repeat step 1 with the obtained quotient (73).
73 ÷ 73 = 1

So, the prime factorization of 146 is, 146 = 2 x 73.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 146 as shown below:

So, the prime factorization of 146 is, 146 = 2 x 73.

#### 3. Find factors of 146 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 146 would be the two numbers which, when multiplied, give 146 as the result.

The following table represents the calculation of factors of 146 in pairs:

Factor Pair Pair Factorization
1 and 146 1 x 146 = 146
2 and 73 2 x 73 = 146

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 146. They are called negative pair factors.

Hence, the negative pairs of 146 would be ( -1 , -146 ) , ( -2 , -73 ) .

#### 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. 146 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, 73, 146 are exact divisors of 146.
• 1 is a factor of every number. Eg. 1 is a factor of 146.
• Every number is a factor of zero (0), since 146 x 0 = 0.

• What two numbers make 146?

Two numbers that make 146 are 2 and 73.

• What is prime factorization of 146?

Prime factorization of 146 is 2 x 73.

• Write some multiples of 146?

First five multiples of 146 are 292, 438, 584, 730.

• Which is the smallest prime factor of 146?

The smallest prime factor of 146 is 2.

• Is 146 a perfect square?

No 146 is not a perfect square.

• What is the sum of all factors of 146?

The sum of all factors of 146 is 222.

• What are factors of 146?

Factors of 146 are 1, 2, 73, 146.

• How do you find factors of a negative number? ( eg. -146 )?

Factors of -146 are -1, -2, -73, -146.

• Is 146 a whole number?

Yes 146 is a whole number.

#### Examples of Factors

Joy wants to calculate mean of all the factors of 146. Help him in finding the mean of 146.

Factors of 146 are 1, 2, 73, 146.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 146 is 1 + 2 + 73 + 146 = 222.
Hence, the mean of factors of 146 is 222 ÷ 4 = 55.50.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 146? Help her in writing all the factors.

Positive factors are 1, 2, 73, 146.
Negative factors are -1, -2, -73, -146.

Joey wants to write all the prime factors of 146 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 146 are 2, 73.
So in exponential form it can be written as 2 x 73.

Kevin has been asked to write 3 factor(s) of 146. Can you predict the answer?

3 factor(s) of 146 are 1, 2, 73.

Sammy is puzzled while calculating the prime factors of 146. Can you help him find them?

Factors of 146 are 1, 2, 73, 146.
Prime factors of 146 are 2, 73

What is prime factorization of 146?

Prime factorization of 146 is 2 x 73 = 2 x 73.

Can you help Rubel to find out the product of the even factors of 146?

Factors of 146 are 1, 2, 73, 146.
Even factors of 146 are 2, 146.
Hence, product of even factors of 146 is; 2 x 146 = 292.