Factors

# Factors of 149 | Prime Factorization of 149 | Factor Tree of 149

Written by Prerit Jain

Updated on: 15 Feb 2023

Contents

### Factors of 149 | Prime Factorization of 149 | Factor Tree of 149

## Factors of 149

Factors of 149 | Factor Pairs of 149 | Prime factors of 149 |

1, 149 | (1, 149) | 149 |

Calculate Factors of

**The Factors are**

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## What are the factors of 149

To find the factors of a number, like 149 for example, you simply have to do some division! Start by dividing it by 2 and see if that divides evenly into the number. If not, keep moving up in prime numbers until one does divide evenly. That will be your first factor! Then take what is left over from that division and see if any other primes can evenly divide it – those new results will also be factors of 149 too! And then finally don’t forget 1 always works as well as itself so they are both considered its own special kind of factor too! All together now: The factors of 149 are 1, 3 (149 divided once by 3 = 49), 49 (divide again by 3 = 16) and lastly we get back to where we started with 149 itself.

## How to Find Factors of 149

**The following are the methods through which you can find the factors of the numbers and their applications to find the factors of 149 also. They are **

- The factor of 149 using the Multiplication Method
- Factors of 149 using the Division Method
- Prime Factorization of 149
- Factor tree of 149

## Factors of 149 using the Multiplication Method

To understand the prime factors of 149, think about it like this: imagine you had a big bag full of candy and needed to share them equally among some friends. You’d need to divide one giant heap into small equal piles. That’s where the trial division comes in! We can use 2 as our divisor (think of that as scissors for creating smaller pieces). But since 149 is not exactly divisible by two we move on to 3 – which means dividing those small piles further would make until there are no remainders left. When all your forks or divides have been used up, voila!, you get an array of numbers from 1-7; these represent each factor present in the original number 🙂

## Factors of 149 Using Division Method

Finding the factors of a number can be useful when you want to break it down into its smallest parts. For example, 149 has three different factors: 1, 3, and 49 – but how do we figure this out? One way is to use something called the division method!

- Let’s try it finding the factor for 149:

Start by dividing 149 by 1 because all numbers are divisible by one. Since there aren’t any leftovers after dividing (aka no remainder), then that means 1 must be a factor of our original number – in this case,149! - Next, let’s divide between two; however, since there IS still some remaining from diving around that time–or again in other words–a “remainder” exists –so 2 cannot possibly make up part of what makes up a rounded-up value like ‘149’, right!?
- So now let’s move on to three…we see once more NO leftover amounts after completing 148 divided quite evenly amongst these fractions. And so on until finally arriving at four as discussed above previously 😉 See how easy maths can sometimes actually feel?

## Prime Factorization of 149

Calculate Prime Factors of

The Prime Factors of 149 =

149

To figure out the prime factorization of a number, like 149 for example, all you need to do is break it down into its smallest parts. So let’s start!

- We divide 149 by 2 – but since this doesn’t work we have to try again with the next prime number which happens to be 3. When we divide that by three? Bam! It works and gives us 49 without any leftovers (also known as remainders).
- Now we move on to seven because it’s also a prime number; when divided into our total from before (49) – surprise: no remainder either! That means 148 = 3 * 7 * 7- so these are our final answers.

In other words, the factors of 149 are made up of three and seven only.

## Factor tree of 149

A prime number can only be divided by itself or 1. To figure out the “prime factors” of any given number, we’ll use something called a Factor Tree! Let’s look at an example to understand how it works:

- Let’s start with the factor tree for 149—the first step is to divide 149 by the smallest prime that will fit (which in this case would be 3). That gives us 49 as our quotient and 3 under it as our divisor on one branch of our tree.
- Then take that same quotient again––49–-and find another small Prime Number which fits into it evenly; 7 divides into 49 without remainder so write down ‘7’ above and below its respective branches like before.
- Once repeated, your resulting answer should tell you all there need about these two numbers multiplied together to give you back your original value –149– because three times seven times seven equals exactly 149!

## Factor Pairs of 149

Calculate Pair Factors of

1 x 149=149

So Pair Factors of 149 are

(1,149)

It’s an easy way to tell if the number is prime or composite.

To figure out the factors, we divide by all numbers that are less than its square root—which for 149 would be any integer up until 12 (excluding itself).

When we do this, the only two integers evenly divided into 149 were 1 and 3 – so those became our factor pairs: (1,149) and (3,49). Since other factors exist beyond 1 & 49 themselves, this makes 149 a composite number!

## Factors of 149 – Quick Recap

**Factors of 149:** 1, 149

**Negative Factors of 149:** -1,-149.

**Prime Factors of 149:** 149

**Prime Factorization of 149:** 149

## Fun Facts of Factors of 149

- 149 is a prime number which means it can only be divided by itself and 1 in whole-number increments.
- The difference between any two consecutive multiples (larger groups) of 3 always has to be 2, but with the addition or subtraction of one more than even this rule doesn’t apply – like when we’re talking about 149!
- This particular composite number isn’t considered a perfect square because its only factors are 1 and three—which makes it totally unique among all other numbers out there!

## Examples of Factor of 149

**1) What are the factors of 149? ****Answer:** The factors of 149 are 1, 3, 7, 21, 49, and 149.

**2) How many prime numbers are factors of 149? ****Answer: **Three prime numbers – 3, 7, and 149 – are factors of 149.

**3) What is the greatest common factor between 42 and 148? ****Answer: **The greatest common factor between 42 and 149 is 7.

**4) What two numbers multiplied together equal 149? ****Answer: **The two numbers which multiplied together equal 149 are 3 and 49 (3 × 49= 147).

**5) If a store sold a product for $149 before tax, how much would it cost with an 8% tax added? ****Answer:** With 8% tax added the product would cost 161.92 dollars ($149 + ($149 x

0.08) = $ 161.92).

**6) Find three consecutive even integers whose sum equals 149.****Answer: **The three consecutive even integers whose sum equals 149 are 74, 76, and 78 (74 + 76 + 78 =228).

**7) Find four consecutive multiples of seven that add up to 149.****Answer: **The four consecutive multiples of seven that add up to 149 are 7, 14, 21, 28 (7 + 14 + 21 + 28 = 70).

**8) Divide 149 by its largest factor to find its smallest factor.****Answer: **Divide 149 by its largest factor which is149to find its smallest factor; the answer is 1.

**9) Find two consecutive odd numbers whose product is equal to 148.Answer: **The two consecutive odd numbers whose product is equal to 148 are 17 and 19 (17 × 19 = 323).

**10) Rachel purchased 4 items at a store for $37 each plus tax at 8%. How much did she spend with tax included?**

Answer:With tax included Rachel spent 153.96 dollars ((4×37)+((4×37)* 0.08)= 153.

Answer:

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## Frequently Asked Questions on Factors of 149

**How many factors does 149 have?**

There are eight different factors of 149.

**What are the factors of 149?**

The factors of 149 are 1, 3, 7, 21, 49, 147, and 149.

**What is the greatest common factor between 149 and 21?**

The greatest common factor between 149 and 21 is 7.

**What two numbers multiplied together equal 149?**

The two numbers which multiplied together equal 149 are 7 and 21 (7 × 21 = 147).

**Divide 149 by its largest factor to find its smallest factor.**

Divide 149 by its largest factor, which is 149, to find its smallest factor; the answer is 1.

**How many prime numbers are factors of 149?**

Three prime numbers – 3, 7, and 49 – are factors of 149.

**Find two consecutive odd numbers whose product is equal to 149.**

The two consecutive odd numbers whose product is equal to 149 are 23 and 25 (23 × 25 = 575).

**Find three consecutive even integers whose sum equals 149.**

The three consecutive even integers whose sum equals 149 are 72, 74, and 76 (72 + 74 + 76 = 222).

**Find four consecutive multiples of seven that add up to 149.**

The four consecutive multiples of seven that add up to 149 are 7, 14, 21, 28 (7 + 14 + 21 + 28 = 70).

**What pair of integers has a product of 149?**

The pair (7,21) has a product of 149.

Written by

Prerit Jain