163 LearnersLast updated on May 26th, 2025
Factors of 174
Factors are the ‘building blocks’ of a number. They are the numbers that can be multiplied together to reach the number you started with. 174 is an interesting number. It is large enough to make you think, but simple enough to learn if you know a few tricks. Let’s dive into it!
What are the factors of 174?
Factors are whole numbers that, when multiplied, the product is equal to 174.
174 is not a prime number, its factors are 1, 2, 3, 6, 29, 58, 87, 174. For every factor, there is a corresponding negative factor, for 174, the negative factors -1, -2, -3, -6, -29, -58, -87, -174.
How to find the factors of 174?
There are various methods we apply to find the factors of any number. Few of them are listed here; multiplication method, division method, prime factors and prime factorization and factor tree method. These are explained in detail below, let’s learn !
Finding Factors Using Multiplication
Step 1: Find all pairs of numbers whose product is 174.
Step 2: All the pairs found represent the factors of 174.
174 is not a prime number. The pair of numbers whose product is 174 is;
1×174=174
2×87 = 174
3×58=174
6×29 = 174
The factors of 174 are 1, 2, 3, 6, 29, 58, 87, 174.
Finding Factors by Division Method
Step 1: Start by dividing 174 with the smallest number, and check the remainders.
Step 2: 174 is not prime, therefore the divisors it has are 1, 2, 3, 6, 29, 58, 87, 174. Any number that is further checked for divisibility leaves behind a remainder.
The factors of 174 are 1, 2, 3, 6, 29, 58, 87, 174.
Prime factors and prime factorization
— 174 is not a prime number.
— The prime factorization of 174 is 2×3×29.
— Factors of 174 are 1, 2, 3, 6, 29, 58, 87, 174.
Factor tree
— In this method, we make branches that extend from the number to express a number as the product of its factors.
— In case of 174, branch will be extended as the number is prime factorized as 2×87→ 3×29. 29 is a prime number and cannot be factored further.
Common mistakes and how to avoid them in factors of 174
We all make mistakes when it comes to finding factors, especially when it comes to numbers like 174. Don’t worry, it is a part of learning. Here are a few common slip-ups we may make, along with tips to avoid them.
Mistake 1
Excluding negative factors
Every positive factor has a corresponding negative factor. Often times, the negative factors are not included.
Factors of 174 Examples
Problem 1
Is 29 a factor of 174?
Divide 174 by 29:
174÷29=6, which is a whole number.
Since there is no remainder, 29 is a factor of 174.
Explanation
If a number divides another number without leaving a remainder, it’s a factor. Here, dividing 174 by 29 results in 6, a whole number, confirming 29 as a factor.
Problem 2
Calculate the sum of all factors of 174.
List the factors of 174: 1, 2, 3, 6, 29, 58, 87, and 174.
Add them up: 1+2+3+6+29+58+87+174=360
The sum of all factors of 174 is 360.
Explanation
To find the sum of all factors, we first identify the factors, then add them. This total, 360, represents the sum of all whole numbers that divide 174 evenly.
Problem 3
What are the common factors of 174 and 87?
Factors of 174: 1, 2, 3, 6, 29, 58, 87, 174.
Factors of 87: 1, 3, 29, 87.
Common factors: 1, 3, 29, and 87.
Explanation
To find common factors, list the factors of both numbers and find those they share. Common factors are numbers that divide both numbers evenly.
FAQs on Factors of 174
1.What could be the GCF of 174?
2. Is 174 a multiple of 7?
3.Is 174 a natural number?
4.Is 174 a perfect square number?
5.What three numbers add up to 174?
Important Glossaries for Factors of 174
- Factors: numbers that divide the given number without leaving a remainder.
- Prime factorization: breaking numbers down into their prime factors.
- Prime factors: Prime numbers that multiply together to form a given number.
- Composite number: Number that has at least more than one divisor other than 1 and the number itself.
Explore More numbers
Previous to Factors of 174
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
