# Factors of 154

Factors of 154 are 1, 2, 7, 11, 14, 22, 77, and 154

#### How to find factors of a number

 1.   Find factors of 154 using Division Method 2.   Find factors of 154 using Prime Factorization 3.   Find factors of 154 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 154

• Divide 154 by 1: 154 ÷ 1 : Remainder = 0
• Divide 154 by 2: 154 ÷ 2 : Remainder = 0
• Divide 154 by 7: 154 ÷ 7 : Remainder = 0
• Divide 154 by 11: 154 ÷ 11 : Remainder = 0
• Divide 154 by 14: 154 ÷ 14 : Remainder = 0
• Divide 154 by 22: 154 ÷ 22 : Remainder = 0
• Divide 154 by 77: 154 ÷ 77 : Remainder = 0
• Divide 154 by 154: 154 ÷ 154 : Remainder = 0

Hence, Factors of 154 are 1, 2, 7, 11, 14, 22, 77, and 154

#### 2. Steps to find factors of 154 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 154 using the division method, follow these steps:

• Step 1. Start dividing 154 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 154, which is 2. Divide 154 by 2 to obtain the quotient (77).
154 ÷ 2 = 77
• Step 3. Repeat step 1 with the obtained quotient (77).
77 ÷ 7 = 11
11 ÷ 11 = 1

So, the prime factorization of 154 is, 154 = 2 x 7 x 11.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 154 as shown below:

So, the prime factorization of 154 is, 154 = 2 x 7 x 11.

#### 3. Find factors of 154 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 154 would be the two numbers which, when multiplied, give 154 as the result.

The following table represents the calculation of factors of 154 in pairs:

Factor Pair Pair Factorization
1 and 154 1 x 154 = 154
2 and 77 2 x 77 = 154
7 and 22 7 x 22 = 154
11 and 14 11 x 14 = 154

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 154. They are called negative pair factors.

Hence, the negative pairs of 154 would be ( -1 , -154 ) , ( -2 , -77 ) , ( -7 , -22 ) and ( -11 , -14 ) .

#### 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. 154 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, 7, 11, 14, 22, 77, 154 are exact divisors of 154.
• 1 is a factor of every number. Eg. 1 is a factor of 154.
• Every number is a factor of zero (0), since 154 x 0 = 0.

#### Frequently Asked Questions

• What are the prime factors of 154?

The factors of 154 are 1, 2, 7, 11, 14, 22, 77, 154.
Prime factors of 154 are 2, 7, 11.

• What is the sum of all factors of 154?

The sum of all factors of 154 is 288.

• What are the pair factors of 154?

Pair factors of 154 are (1,154), (2,77), (7,22), (11,14).

• What two numbers make 154?

Two numbers that make 154 are 2 and 77.

• What are multiples of 154?

First five multiples of 154 are 308, 462, 616, 770.

• Is 154 a perfect square?

No 154 is not a perfect square.

• Which is greatest factor of 154?

The greatest factor of 154 is 77.

• How do you factors of 154?

Factors of 154 are 1, 2, 7, 11, 14, 22, 77, 154.

• What are five multiples of 154?

First five multiples of 154 are 308, 462, 616, 770, 924.

#### Examples of Factors

Can you help Rubel to find out the product of the even factors of 154?

Factors of 154 are 1, 2, 7, 11, 14, 22, 77, 154.
Even factors of 154 are 2, 14, 22, 154.
Hence, product of even factors of 154 is; 2 x 14 x 22 x 154 = 94864.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 154? Help her in writing all the factors.

Positive factors are 1, 2, 7, 11, 14, 22, 77, 154.
Negative factors are -1, -2, -7, -11, -14, -22, -77, -154.

How many factors are there for 154?

Factors of 154 are 1, 2, 7, 11, 14, 22, 77, 154.
So there are in total 8 factors.

Sammy is puzzled while calculating the prime factors of 154. Can you help him find them?

Factors of 154 are 1, 2, 7, 11, 14, 22, 77, 154.
Prime factors of 154 are 2, 7, 11

Joey wants to write all the prime factors of 154 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 154 are 2, 7, 11.
So in exponential form it can be written as 2 x 7 x 11.

What is prime factorization of 154?

Prime factorization of 154 is 2 x 7 x 11 = 2 x 7 x 11.

Can you help Rubel to find out the product of the even factors of 154?

Factors of 154 are 1, 2, 7, 11, 14, 22, 77, 154.
Even factors of 154 are 2, 14, 22, 154.
Hence, product of even factors of 154 is; 2 x 14 x 22 x 154 = 94864.

Share your expierence with Math-World