Factors

# Factors of 140 | Prime Factorization of 140 | Factor Tree of 140

Written by Prerit Jain

Updated on: 15 Feb 2023

Contents

### Factors of 140 | Prime Factorization of 140 | Factor Tree of 140

## Factors of 140

Factors of 140 | Factor Pairs of 140 | Prime factors of 140 |

1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70 and 140 | (1,140), (2, 70), (4, 35) (5, 28), (7, 20) and (10, 14) | 2 x 2 x 5 x 7 |

Calculate Factors of

**The Factors are**

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## What are the factors of 140

140 has several positive integer factors and can be broken down using prime factorization. The list of its factors includes 1, 2, 4, 5,7 8 10 14 20 28 35 40 70 & 140 – an impressive 12 in total! All you need to do is combine any combination of these together like so: 2*5*7 = 70 – a perfect example which also happens to be one of the many factors that make up 140.

## What are the factors of 140

140 have several positive integer factors and can be broken down using prime factorization. The list of its factors includes 1, 2, 4, 5 ,7 8 10 14 20 28 35 40 70 & 140 – an impressive 12 in total! All you need to do is combine any combination of these together like so: 2*5*7 = 70 – a perfect example which also happens to be one the many factors that make up 140.

## How to Find Factors of 140

The factors of a number can be found through the following methods and through the same methods we can also find the factors of 140. They are as follows:

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

## Factors of 140 using Multiplication Method

To break down the number 140 into its factors, start by finding all of the pairs that can multiply together to make it. Begin with 1 and 140 – if you multiple them both together you will get your result: 140! Then try 2 and 70; are they a pair? Yes, when multiplied these two numbers equal our original target total-140 again. Keep going in this fashion until every factor has been checked for accuracy against what we’re looking for – once each one is confirmed as true (or false) then identify those which resulted in “true” products being formed – they are your answer’s set of factors!

Using this method, you can find all the factor pairs of 140:

(1, 140)

(2, 70)

(4, 35)

(5, 28)

(7, 20)

(8, 17.5)

(10, 14)

(14, 10)

(20, 7)

(28, 5)

(35, 4)

(70, 2)

(140, 1)

All of these pairs, when multiplied together, will give the product 140.

## Factors of 140 Using Division Method

Have you ever wanted to learn how to find the factors of a number? The division method can be used for this. Start by taking your chosen number (like 140) and divide it by 1 – if the result is even, then you’ve found one factor! If not, move on with 2 as your divisor; rinse and repeat until reaching that same starting number itself. With this approach applied to 140 – all these numbers are now known: 1, 2, 4 ,5,7 ,8,1014 20 28 35 70 & 140 –all evenly dividing into our initial figure without leaving any remainder behind.

## Prime Factorization of 140

Calculate Prime Factors of

The Prime Factors of 140 =

2 x

2 x

5 x

7

Prime factorization is a key mathematical concept that helps break down any number into its core components, each of which are prime numbers. For example, the number 140 can be expressed as 2^3 * 5*7 – indicating that it consists of 3 factors or multiples of two multiplied by one multiple each for five and seven respectively. This formula may only work in this exact combination because there is no other case where you could multiply something else along with 2^2 to arrive at the same result! Consequently, Prime Factorization provides an effective way to further investigate positive whole numbers and understand more about them on a deeper level.

## Factor tree of 140

To find the prime factorization of a number, such as 140 in this case, you can use what is known as a ‘factor tree’. To create one for any given base number (e.g.,140) simply write it at the top and start dividing that by its smallest prime factors until all terms are factored into numbers that cannot be divided further- i.e., primes! For example; splitting 140 with 2 results in 70 – divide that again with another 2 gives 35 while 5 & 7 being their own unique primes makes up the last two branches on your factor tree to complete our desired result: ‘140 = 2*2*5*7’

## Factor Pairs of 140

Calculate Pair Factors of

1 x 140=140

2 x 70=140

4 x 35=140

5 x 28=140

7 x 20=140

10 x 14=140

14 x 10=140

20 x 7=140

28 x 5=140

35 x 4=140

70 x 2=140

So Pair Factors of 140 are

(1,140)

(2,70)

(4,35)

(5,28)

(7,20)

(10,14)

(14,10)

(20,7)

(28,5)

(35,4)

(70,2)

Knowing the factor pairs of a number can be quite helpful. Take 140 as an example: it has twelve different sets of factors, which are (1,140), (2,70),

(4,35), and so on up to (140, 1). To get these 12 answers you could either list out all possible combinations or figure them out using prime numbers; in this case, 2³ * 5 * 7 is what makes up 140’s very own unique set of factors!

## Factors of 140 – Quick Recap

**Factors of 140:** 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70 and 140

**Negative Factors of 140:** -1, -2, -4, -5, -7, -10, -14, -20, -28, -35, -70, -140.

**Prime Factors of 140:** 2 x 2 x 5 x 7

**Prime Factorization of 140:** ** **2 x 2 x 5 x 7

## Fun Facts of Factors of 140

- 140 is not a prime number, which means that it has more than two positive integer factors. In fact, 140 has 12 positive integer factors.
- The prime factorization of 140 is 2^3 * 5 * 7. This means that 140 can be expressed as the product of three factors of 2, one factor of 5, and one factor of 7.
- 140 is not a perfect square, which means that it cannot be expressed as the product of two equal integers. For example, 4 is a perfect square because it can be expressed as 2 * 2.
- 140 is an even number, which means that it is divisible by 2.
- 140 is not a multiple of 3, 5, or 7.

## Examples of Factor of 140

**1. Joana has 140 pieces of candy, how many bags of 5 can she make?**

**Answer: **Joana can make 28 bags of 5 pieces of candy if she has 140 pieces (140 ÷ 5 = 28 with the remainder 0).

**2. Emma needs to share her $140 among 4 friends. How much money will everyone receive?**

**Answer:** Everyone will receive $35 if Emma shares her $140 among 4 friends ($140÷4=35).

**3. If there are 27 students in the class and each student needs 10 textbooks, how many textbooks do they need in total? **

**Answer: **The class needs 270 textbooks in total if there are 27 students and each student needs 10 textbooks (27 x 10 = 270).

**4. Jane is making a cake that requires 7 eggs for every 6 cups of flour. How many eggs does she need if she uses 8 cups of flour? **

Answer: Jane needs 8 eggs if she uses 8 cups of flour for a cake that requires 7 eggs per 6 cups (7 x 8 = 56, subtract 48 equals 8).

**5. What is the greatest common factor for 140? **

Answer: The greatest common factor (GCF) for 140 is 20.**6) David wants to buy 3 shirts which cost 40 dollars each, how much money must he pay? ****Answer: **David must pay$ 120 if he wants to buy 3 shirts which is 40 dollars each ($40×3=120 ).

7) Find all factor pairs for the number 140 using exponential notation for any prime factors that appear more than once in the factor tree**Answer: **The factor pairs for the number 140 using exponential notation are1x140or1⁰x14⁰

**8) If 143 apples are divided into groups of 18, how much will each group receive? **Answer: Each group will receive 8 apples if you divide 143 apples into groups of 18(143÷18=8with remainder 7 ).

**9)If Jullian bought 128 items and expects to receive an additional 12 items in his next order delivery, how many items will be included in his next order delivery? Answer: **Jullian’s next order delivery will include 12 items if he bought 128 items(128+12=140 ).

**10) Dan wants to buy a toy train model set costing 139 dollars but he only has 32 dollar bills, how many bills does Dan need? Answer:**Danneeds5billsifhewantstobuyatoytrainmodelsetcost ing139dollarsandheonlyhas32dollarbills(32×5=160 , subtract 21 equals 139 ).

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## Frequently Asked Questions on Factors of 140

**What are the factors of 140?**

The factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 40, 70 and 140.

**What is the greatest common factor (GCF) for 140?**

The greatest common factor (GCF) for 140 is 20.

**What is the least common multiple (LCM) for 140?**

The least common multiple (LCM) for 140 is 840.

**How many factors does 140 have?**

There are 12 factors that 140 has which include 1, 2, 4, 5, 7 , 10 , 14 , 20 , 28 , 35 , 40 , 70, and 140.

**Does 139 have any prime factors?**

Yes, 139 has two prime factors – 3 and 43 as 3×43 = 129 + 10 = 139.

**How can I use exponential notation to write out the different factor pairs of 140?**

The factor pairs of 140 written in exponential notation are 1×140 or 1⁰ x14⁰ .

** Is there a formula for finding all the divisors of a number?**

Yes, there is a formula for finding all of the divisors of a number which states that the sum of all positive divisors including one and excluding the number itself will be equal to twice the number itself (a + b + c… = 2n). For example with an input number such as n=140; Divisors (1+2+4+5+7+10+14+20+28+40+70)=140 x 2 = 280.

**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 calculated their greatest common factor by using the Euclidean Algorithm.

**If Donna wants to buy 8 books each costing $17 dollars total how much money must she pay?**

Donna needs to pay $136 if she wants to buy 8 books each costing $17 dollars ($17×8=136 ).

**Find all factor pairs for the number 139 using exponential notation for any prime factors that appear more than once in the factor tree.**

The factor pairs for the number 139 using the exponential notion are 1x139or1⁰x139.

Written by

Prerit Jain