Factors

# Factors of 154 | Prime Factorization of 154 | Factor Tree of 154

Written by Prerit Jain

Updated on: 12 Aug 2023

Contents

### Factors of 154 | Prime Factorization of 154 | Factor Tree of 154

## Factors of 154

Factors of 154 | Factor Pairs of 154 | Prime factors of 154 |

1, 2, 7, 11, 14, 22, 77, 154 | (1, 154), (2, 77), (7, 22), (11, 14) | 2 x 7 x 11 |

Calculate Factors of

**The Factors are**

Looking to Learn Math? Book a Free Trial Lesson and match with top Math Tutors for concepts, homework help, and test prep.

## What are the factors of 154

Have you ever wanted to know which numbers can be multiplied together to get a specific number? Well, one way we can figure out what those two numbers are is by finding the factors of that given number! Let’s take 154 as an example.

First off, we need to come up with all the potential possibilities for multiplying two whole numbers together and getting 154 – these would be our ‘factors’. To do this efficiently, let’s first use something called square root: it means dividing any squared (for ex., 4 x4) number until you get down its “roots”. It just so happens that when we find the square root of 154, it turns out around 12.3 — so if we create a list from 1-12 then 3 times 51 will equal exactly 154!. This means both 3 and 51 are Factors of 154. We also already know that anything divided by itself always equals 1; in other words… since every prime Factorization only has 2 totals – itself plus 1–this tells us right away that anytime dealing with a prime number such as 154 his factorization must include only himself +1. And there you have All possible answers for what divides into 154 are:1and154.

## How to Find Factors of 154

The major 4 methods through which you can find the factors of 154 are as mentioned below:

- Factor of 154 using Multiplication Method
- Factors of 154 using Division Method
- Prime Factorization of 154
- Factor tree of 154

## Factors of 154 using Multiplication Method

Did you know there’s a fun and easy way to find all the factors of any number? All it takes is breaking down the big numbers into smaller ones, then doing some quick division. Let’s use 154 as an example!

- When we divide 154 by each integer between 1 and its square root (12), which are 2, 3, 4… 12 in this case – if there’s no remainder left over that means these integers can be multiplied together to make up our original number of 154. This makes them “factors.”
- In the end for Number154; those two factors were 2 & 7 with 11 also being able to multiply too due to 27*7 = 117 so 77 x 2 = 157 or reversed with 17X9=153 So only four values could amount up to what would equal 153-157 not including negative versions since they don’t help us out here either.
- If accepted on paper Five value, therefore, must go but one shall stay when testing Prime factorization: The prime factorization has both divisibility levels alongside unique hard-coded testable answers per problem set. For 156 it was determined through math components such as multiplication & Division methods arriving at pf(2711) providing hidden ridges within numeric palettes forming secret passageways inside your mindscape.

## Factors of 154 Using Division Method

To find the factors of 154, you can use multiplication!

- First, we start by finding what numbers can go into 154 to make it even. To do this quickly, take the square root of 154 which is around 12.3 – so your list starts at 1 and ends at 13 (just round up).
- Now divide each number in that range into 154- if there’s no leftover then those are “factors”. For example, when dividing 7 into 154 it goes 22 times with 0 remaining – this means that both 7 and 22 are factors of 154! And sure enough, using our multiplication method you will have 2,7,11 as 3 different factors for a total sum that add up to 164!!

## Prime Factorization of 154

Calculate Prime Factors of

The Prime Factors of 154 =

2 x

7 x

11

Prime factorization is a way of breaking down any number into only prime numbers, which are numbers that can’t be divided by anything other than itself and one. For example, if you want to find the ‘building blocks’ for 154, start with two as it’s the smallest prime number (since 1 isn’t considered a prime). Divide 154 in half so you get 77: 2 x 77 =154. Now divide your answer further – since 7 is another small prime figure we’ll use this instead; 76 ÷7=11 11 being another perfect Prime!

So now our math recipe looks like this: 2x7x11=154. You’ve broken down your original big problem into smaller parts using those pesky little primes until all pieces were solved – giving us the answer of how far back our starting point was made up from different building blocks –2 times 7 equals 14 & 14 times 11 will give us out final sum total of just plain ol’ ordinary lowdown dirty 154 !

## Factor tree of 154

A factor tree is a really cool tool that can be used to help us find the prime factors of any number! Let’s use it to figure out the prime factors for 154. We start by writing 154 at the top of our tree, and then we draw two branches coming from there with numbers 2 and 77 on either side. That’s because those are the smallest whole numbers that divide into 154 without any leftover (called no remainder). Next, since 77 isn’t a prime number like 2 was, we break down each branch further until both sides have only prime numbers listed: 7 and 11 in this case. Voila! The process looks something like this: 154 = 2 x 7 x 11 – so these three were all the unique combinations of smaller digits that multiplied together and gave us our original number.

## Factor Pairs of 154

Calculate Pair Factors of

1 x 154=154

2 x 77=154

7 x 22=154

11 x 14=154

14 x 11=154

22 x 7=154

77 x 2=154

So Pair Factors of 154 are

(1,154)

(2,77)

(7,22)

(11,14)

(14,11)

(22,7)

(77,2)

If you want to figure out the factor pairs of a number, like 154 in this example, then it’s really simple. First, start by dividing that same number (in our case – 154) over each integer from 1 up until its square root! This is because if we kept going beyond the square route there would be no more integers for us to divide with and so nothing new or unique can come out of those divisions anymore… Anyhow- once noticing whether or not there was any remainder when doing these division calculations write down both your dividend and divisor as a pair. These will make up all the factor pairs associated with 154 which are:

(1,154); (2,77),; (7,22); (11,14 );( 22,7 )and last but not least – ( 77,2). There may seem like some duplications since seeing something such as “( 2 & 77)”, alongside another thing saying “(77&2)” — don’t let yourself get confused though ’cause they simply just mean exactly the same thing only flipped around differently!

## Factors of 154 – Quick Recap

**Factors of 154: **** **** ****1, 2, 7, 11, 14, 22, 77, 154**

**Negative Factors of 154: ****-1, -2, -7, -11, -14, -22, -77, -154**

**Prime Factors of 154: 2 x 7 x 11**

**Prime Factorization of 154: 2 x 7 x 11**

## Fun Facts of Factors of 154

- The number 154 is made up of parts.
- First, it has two prime numbers – 2 and 7- which can be multiplied together to make the total (2 x 7 = 14). But that’s not all!
- If we multiply each one by an additional prime number 11, then we get our final answer: 2 x 7 x 11 = 154. This means there are 6 different factors for this special number; 1,2,7,11,14, and 77.
- And if you add them all up– from smallest factor “1” to biggest factor “154,” you’ll end up with 206 as your grand total! That sum above the original value? We call that its “aliquot sum”.

## Examples of Factor of 154

**1) What is the greatest common factor between 70 and 154?**

**Answer:** The greatest common factor between 70 and 154 is 2.

**2) Find four consecutive multiples of seven that add up to 154.****Answer:** The four consecutive multiples of seven that add up to 154 are 7, 14, 21, and 28 (7 + 14 + 21 + 28 = 91).

**3) What two numbers multiplied together equal 154?****Answer:** The two numbers which multiplied together equal 154 are 6 and 26 (6 × 26 = 156).

**4) Divide 154 by its largest factor to find its smallest factor. ****Answer: **Divide 154 by its largest factor which is 26to find its smallest factor; the answer is 6.

**5) If a store sold a product for $154 before tax, how much would it cost with 8% tax added?****Answer:** With 8% tax added the product would cost 166.72 dollars ($154 + ($154 x 0.08)= 166.72).

**6) What are the factors of 154?****Answer:** The factors of 154 are 1, 2, 3, 6, 17, 34, 51, and 102.

**7) How many prime numbers are factors of 152? ****Answer:** Four prime numbers – 2, 3, 17, and 71 – are factors of 154.

**8) Find three consecutive even integers whose sum equals 154.****Answer: **The three consecutive even integers whose sum equals 154 are 76, 78, and 80(76+78+80=234).

**9) Find two consecutive odd numbers whose product is equal to 155.****Answer: **The two consecutive odd numbers whose product is equal to 155 are 19 and 21(19×21=399).

**10) Rachel purchased 5 items at a store for $31 each plus tax at 8%. How much did she spend with tax included?Answer:** With tax included Rachel spent 167.28 dollars ((5×31)+((5×31)* 0.08)= 167.28).

Looking to Learn Math? Book a Free Trial Lesson and match with top Math Tutors for concepts, homework help, and test prep.

## Frequently Asked Questions on Factors of 154

**What are the factors of 154?**

The factors of 154 are 1, 2, 3, 6, 17, 34, 51, and 102.

**How many prime numbers are factors of 154?**

Four prime numbers – 2, 3, 17, and 71 – are factors of 154.

**What is the greatest common factor between 70 and 154?**

The greatest common factor between 70 and 154 is 2.

**Find three consecutive even integers whose sum equals 154.**

The three consecutive even integers whose sum equals 154 are 76, 78 , and 80(76+78+80=234).

**Find two consecutive odd numbers whose product is equal to 155.**

The two consecutive odd numbers whose product is equal to 155 are19and21(19×21=399).

**How many multiples of seven add up to 154?**

Four multiples of seven add up to 154; they are 7, 14, 21, and 28 (7 + 14 + 21 + 28 = 91).

**If a store sold a product for $154 before tax, how much would it cost with an 8% tax added?**

With 8% tax added the product would cost

166.72 dollars ($154 + ($154 x 0.08)= 166.72).

**What two numbers multiplied together equal 154?**

The two numbers which multiplied together equal 154 are 6 and 26 (6 × 26 = 156).

**Divide 154 by its largest factor to find its smallest factor.**

Divide 154 by its largest factor which is 26to find its smallest factor; the answer is 6.

**Rachel purchased 5 items at a store for $31 each plus tax at 8%. How much did she spend with tax included?**

With tax included Rachel spent 167.28 dollars ((5×31)+((5×31)*

Written by by

Prerit Jain