Factors

# Factors of 145 | Prime Factorization of 145 | Factor Tree of 145

Written by Prerit Jain

Updated on: 15 Feb 2023

Contents

### Factors of 145 | Prime Factorization of 145 | Factor Tree of 145

## Factors of 145

Factors of 145 | Factor Pairs of 145 | Prime factors of 145 |

1, 5, 29, 145 | (1,145) (5,29) (29,5) | 5 x 29 |

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 145

Finding the factors of 145 is a matter of breaking it down into its smallest ‘building blocks.’ Using factorization, these building blocks can be determined by listing out the pairs in order from smallest to largest. For this case, those pairs would be (1×145), and (5×29). All together that makes 1, 5, 29 and 145 all possible factors for 143.

## How to Find Factors of 145

Here are four methods that you can use to find the factors of 124:

- Factor of 124 using Multiplication Method
- Factors of 124 using Division Method
- Prime Factorization of 124
- Factor tree of 124

## Factors of 145 using Multiplication Method

To find the factors of 145, you must first figure out its prime factorization. This is done by dividing the number (145) with a small prime like 2 or 3 until only another single prime remains in your answer- 5 x 29 = 145. After that all possible combinations can be found simply by multiplying each individual factor together – which gives us 1,5 ,29 and finally 147 itself as our list of factors for this particular number!

## Factors of 145 Using Division Method

To find the factors of a given number, start by dividing it by 1 to see if that is an answer. If not, continue checking each integer up until you reach the square root of your original number. When one divides evenly with no remainder into this initial number then it has been identified as a factor! In our example we chose 145 and found its smallest possible factor was 5 when divided in half yields 29 – proving itself as an acceptable solution for divisibility on further investigation !

## Prime Factorization of 145

Calculate Prime Factors of

The Prime Factors of 145 =

5 x

29

To express a number like 145 as the product of its prime factors, you can use factorization. This involves dividing the number by small prime numbers and continuing to divide until no other primes are possible. In this case, we divided 145 by 2 and 3 first both of which were not factors – then 5 was found to be a factor when it was divided with 29 being the remaining result making that another factor too. Therefore when all these divisions have been completed, it is clear that 5 x 29 =145 thus proving that these two primes make up this particular number!

## Factor tree of 145

To better understand factor trees and how they work, let’s take a look at the one for 145. The tree is made up of two parts:145 divided by 5 gives us 29 as the final result – which itself is a prime number – meaning that this number can’t be broken down any further. This tells us right away that the factors (or numbers) we need to multiply together in order to get our original number are 5 and 29; multiplied together these give us 145!

To create your own factor tree you would use something called ‘factorization’. This method involves dividing whatever your chosen starting point (in this case it was 145) with 2 or another small prime number until all you have left is a single prime as its answer before working backward from there.

## Factor Pairs of 145

**{Insert Factor Pairs Calculator}**

To figure out all the pairs of positive integers that can be multiplied to make 145, we have to first look at its prime factorization. When you break down a number into its two lowest possible factors (called prime numbers), in this case 11 and 13 are both needed for it equal exactly 145. That’s why these four combinations work: 1×145; 11×13; 13×11; and even itself multiplied by iself – 145 x145! Prime Numbers only have 2 factors so since there are 4 possibilities here with different integer pairings, it’s safe to say that this isn’t one of them- making our final answer clear – 145 is not a Prime Number.

## Factors of 145 – Quick Recap

**Factors of 145:** 1, 5, 29, 145

**Negative Factors of 145:** -1, -5, -29, -145.

**Prime Factors of 145:** 5 × 29.

**Prime Factorization of 145:** ** **5 × 29.

## Fun Facts of Factors of 145

- The factors of 145 are 1, 5, 29, and 145.
- 145 is the sum of the consecutive integers from 8 to 14 (8 + 9 + 10 + 11 + 12 + 13 + 14 = 145)
- 145 is also the sum of the cubes of 3 and 4 (3^3 + 4^3 = 27 + 64 = 91 + 54 = 145).
- 145 can be expressed as the difference of two squares: 145 = 12^2 – 7^2 = 144 – 49 = 145.
- 145 is the largest 2-digit prime number that is the sum of two prime numbers, 5 and 29.
- 145 is an automorphic number, it’s last two digits of its square is the same as its own number(145^2= 21025, last two digits are 25)

145 is a Harshad number. A Harshad number is a number that is divisible by the sum of its digits. The sum of the digits of 145 is 1 + 4 + 5 = 10, and 145 is divisible by 10, so it is a Harshad number. - 145 is an odd number and cannot be expressed as the sum of consecutive numbers.

## Examples of Factor of 145

**1. If John has 145 pieces of candy, how many packages can he make if he wants to put 10 pieces in each package?**

**Answer:** John can make 14 packages (145/10 = 14).

**2. Find the greatest common factor between 144 and 145? **

**Answer: **The greatest common factor between 144 and 145 is 1.

**3. What is the least common multiple (LCM) for 144 and 145? **

**Answer:** The least common multiple (LCM) for 144 and 145 is

2160.**4) How much money will someone have to pay if they buy 15 boxes of chocolates costing $19 each? ****Answer: **They pay a total of $285 if they buy 15 boxes costing$19each ($ 19×15=285).**5) How many divisors does 145 have? ****Answer:**145 has 8 divisors which are1 ,3 ,5,9,15,45 and145.**6) What is the sum of all positive divisors excluding one and excluding the number itself? **Answer: The sum of all positive divisors excluding one and excluding the number itself is equal to the square of the number(21025).

**7) If a person has 145 minutes on the phone, how much time do they have in hours? Answer:**The person has 2 hours and 25 minutes (145 minutes/60=2hr25min ).

**8) Is it possible to check if two numbers are relatively prime without calculating their greatest common divisor?**

**Answer:**Yes, it is possible to check if two numbers are relatively prime without having to calculate their greatest common divisor rowing any of the definitions provided by the relevant Math literature.

**9) Find all factor pairs for the number 149 using exponential notation for any prime factors that appear more than once in the factor tree.**

**Answer: **The factor pairs for the number 149 using exponential notation are 1x149or1⁰x149,3x49or3⁰x49and7x21or7¹x21.**10) If I have 148 sticks can I make 4 candles each with 37 sticks? Answer: **Yes, you have enough supplies as 148 has 8 factors which include these needed to produce four candles with 37sticks-namely7(seven folds of our candles owing to 37 sticking being equal to 4×7+5as4×7=128) and 5(five folds of 20 owing to 37 sticking being equal to 2×20+17a s2×20=40).

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 145

**What are the factors of 145?**

The factors of 145 are 1, 11, 13, and 145

**Is 142 a factor of 145?**

No, 142 is not a factor of 145.

**What is the highest common factor between 145 and 142?**

The highest common factor between 145 and 142 is 1.

**What is the least common multiple (LCM) for 145?**

The least common multiple (LCM) for 145 is

819.

**How many divisors does 141 have?**

141 has 4divisors which are1 ,11 ,13, and145.

**Is it possible to check if two numbers are relatively prime without calculating their greatest common factor?**

Yes, it is possible to check if two numbers are relatively prime without having to calculate their greatest common factor rowing the Euclidean Algorithm.

**If I have 140 sticks can I make 4 candles each with 35 sticks?**

No,youhavenotenoughsuppliesas140has7factorswhichinclude1 ,2 ,5 ,7 ,10,14and20-thus meaning you cannot make four candles with140 sticks(14×10=140).

**How much money must be paid if someone wants to buy 16 boxes of chocolates costing $17 each?**

They need to pay a total of $272 if they want to buy 16 boxes of chocolates costing $ 17 each ($17×16=272).

**What is the sum of all positive divisors including one and excluding 141 itself?**

The sum of all positive divisors including one and excluding the number 141 itself is equal to three times the number itself(423).

**Find all factor pairs for the number 144 using exponential notation for any prime factors that appear more than once in the factor tree**

The factor pairs for the number 144 using exponential notation are1x144or1⁰x144.

Calculate Pair Factors of

1 x 145=145

5 x 29=145

29 x 5=145

So Pair Factors of 145 are

(1,145)

(5,29)

(29,5)

Written by

Prerit Jain