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Factors of 167 | Prime Factorization of 167 | Factor Tree of 167

Written by Prerit Jain

Updated on: 17 Aug 2023


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Factors of 167 | Prime Factorization of 167 | Factor Tree of 167

Factors of 167 | Prime Factorization of 167 | Factor Tree of 167

Factors of 167Factor Pairs of 167Prime factors of 167
167 =   1, 167(1, 167)167=  167

What are the factors of 167

Calculate Factors of

The Factors are


167 belongs to a special set of numbers called Prime numbers which have only two factors, they can be divided by itself and 1 unlike the Rest of them (non-primes) which has more than just those two factors! 167 is a prime number because it has only factors: 1, 167- you can try and divide it ‘n’ number of times  – if any factor between 2 and its square root isn’t an even fit, then we have a prime!

How to Find Factors of 167

The four different methods that we 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 167 using Multiplication Method

Easy way to check any number whether it is prime or not ! using a method called trial division. Divide the number by any two numbers between two and square root of the original number (for 167,it is  between 2 and 12).  if they bring no remainders then the original number is a prime number! There are other methods too which are a bit more complicated, which include  AKS primality test or Miller-Rabin primality test. Which aren’t that optimal for smaller numbers. Remember when trying to find out whether 167 is prime or not : divide it by all other whole numbers up until its square root !

Factors of 167 Using Division Method

Prime numbers are so special as they only have two “friends” – themselves and the number 1. Easy way to say if a number like 167 is a prime is by dividing it with each integer between 1 to itself, in this case from 1-167. If both of these divisions has no remainder left over after they divide then we know it’s a true friend! 

Prime friends play an important role because they’re used  to keep things safe when transferring data or sending messages across computers known as cryptography. So just know,  when looking at any potential new pals out there make sure your friendship isn’t too divisible; careful before commitments!

Prime Factorization of 167

Calculate Prime Factors of

The Prime Factors of 167 =



A prime number cannot be broken down into smaller parts without leaving a remainder . Let 167 be an example – its prime factorization (breaking the original number down as small as possible) is 167; so to break this big number apart, there’s only one way of using the same exact number!

You can also try drawing out a tree-like diagram called “factor trees”, with167 at the top of the tree – if we do that for 167  we would end up having on our ‘tree’ nothing but 166 alone !

Factor tree of 167


A factor tree is a way of  breaking numbers into their smallest parts. Say 167, it would be written on the top: like 167.

Numbers that can’t be broken down anymore are known as prime factors – as we can’t take anything away from 167 making  it smaller, then it’s known its prime factorization (the method  of breaking something down) is itself! This means, without being divided further-167 IS A PRIME NUMBER!

Factor Pairs of 167

Calculate Pair Factors of

1 x 167=167

So Pair Factors of 167 are



The unusual numbers which are special and can only be divided by itself and 1 are named prime numbers. Prime numbers are the ones that have two factors: one and itself ! That means the factor pair of 167 will always be (1,167).

But the non-prime or composite numbers have lots more than two factors – they always end up with many combinations hence, harder to calculate. The three main ways to find all these combos for any kind of composite numbers include multiplication method, division method & prime factorization methods!

Remember, when it comes down to prime numbers they never give anything away besides their own unique combo as they either divide evenly into another whole exact same prime OR don’t agree at all which shows their uniqueness among all numbers !!!

Factors of 167 – Quick Recap

Factors of 167: 1,167

Negative Factors of 167:  -1, -167.

Prime Factors of 167:  167

Prime Factorization of 167: 167

Fun Facts of Factors of 167

Let’s break down the number 167. First, a factor of any number is just that part or parts which divides evenly into it. So for our 167 example, 1 times 7 × 23 equals 167 then they are the factors. The sum of all those factors adds up to 220 (1 + 7 + 23 +167=220). Now when you add two prime numbers together like we have here with 2 and 67 which are also  prime numbers. Prime means something special as it leaves remainder if  you divide them by anything other than themselves or one …so in this case the only two ways to get exactly equal shares of 167 would be to keep dividing them up until each side has 11 pieces since both are divisible by 11 without leaving anything behind . Most sets don’t usually have more than four factors but in this case there is! as it’s an odd combination resulting in 4 different combinations!! 

Examples of Factor of 167

1) If Thomas has 167 apples and wants to evenly divide them into 3 separate containers, how many apples will he have in each container?

Answer: Thomas will have 55 apples in each of the containers. 

2) Maria has a box of 167 marbles. She needs to equally distribute them among 4 friends. How many marbles can each friend receive?

Answer: Each friend can receive 41 marbles from Maria’s box. 

3) Joe has a pocket full of 167 coins. He needs to divide them into groups of 7 for a game with his friends. How many groups does he need?

Answer: Joe will need 24 groups of coins with 7 coins in each group for the game. 

4) Greg is selling 167 individual pieces of candy for 10 cents each. How much money will he make in total? 

Answer: Greg will make $

16.70 from selling all pieces of candy at 10 cents each. 

5) Lindy needs to buy 167 pencils equally distributed among 9 classrooms in her school. How many pencils should she buy for each classroom? 

Answer: Lindy should buy 18 pencils for every classroom she buys them for, so that they are equally distributed among the 9 classrooms in her school..  

6) John wants to provide snacks for his soccer team which consists of 23 players. He has 167 cookies altogether, how many cookies should he give out per player?

Answer: John should give out 7 cookies per player on his soccer team, so that all 23 players are provided an equal amount and also so all 167 cookies are used up accordingly!

7) Jayden had 168 items but lost one item during a game, how many factors now exist with the remainder being 167?  

Answer: With the remaining number being 167, there still exists four factors which are 1, 7, 23, and167 .  

8 ) Mary was asked to fill up 168 balloons but realised she only had enough material for two-thirds of it, which would be exactly 112 balloons; what is the other factor besides 112 that would fulfil this exact request if she had enough material available?    

Answer: The other factor besides 112 needed to fulfil this exact request would be 56; as 56 +112 equals 168 balloons requested by Mary. 

9) Joan was given 11 bags filled with cards and needed help dividing it equally between 2 people but found out there were actually only 154 cards altogether instead of 168 – what is the new factor if 154 cards were divided amongst two people instead ?     

Answer: The new factor if 154 cards were divided amongst two people instead would be 77; since 77 plus 77 equals 154 cards altogether!  

10) Sarah bought three boxes containing 58 items each and another containing 44 items from a store; what is the highest common factor between 161 (3×58), 162 (3×58+1), 163 (3×58+2), 164 (3×58+3), 165 (3×58+4), 166 (3×58+5), and167(44)?    Answer: The highest common factor between these numbers is 1; as no prime factors exist between any two numbers except when one number subtracts from itself or else when multiplying it by 1 – resulting in 1 being its highest common denominator!

Frequently Asked Questions

What are the factors of 167? 

Answer: The factors of 167 are 1, 7, 23, and 167.

How many factors does 167 have? 

Answer:167 has four factors; these being 1, 7, 23, and 167.  

What two prime numbers multiplied together make up 167? 

Answer: The two prime numbers that make up 167 are 7 and 23. 

If one number is decreased by 10, what will be its greatest common factor with 167?   

Answer: The greatest common factor between the two numbers will be 1 or less , as any number minus 10 will have a highest common factor with 167 of 1 or less. 

What are all the combinations of two prime numbers multiplying together to produce167? 

Answer: The combinations of two prime numbers multiplying together to produce 167 are 7 x 23 and 1 x 167.  

What is the greatest common factor for 167 and another number if both numbers can be divided evenly by 2 and 11?  

Answer: The greatest common factor between the two numbers is 22; as both numbers can be divided evenly by 2 and 11.  

If you half the dividend and quotient  of the expression 167÷21 what is the number you will obtain? 

Answer: You will obtain 8; halving the dividend (7), and then halving the quotient (21), results in 8.

What is the sum of all factors of 167 including itself?     

Answer: The sum of all factors of 166 including itself is 220. 

If 162x something equals 167 what is the unknown value?

Answer: The unknown value is 5, as 162×5 =166.  

If you divide 3 into 167 how many times can it go in evenly?

Answer: 3 can go into 166, 55 times evenly.

Written by

Prerit Jain

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