159 LearnersLast updated on May 26th, 2025
Factors of 374
Factors of 374 are numbers that can divide 374 completely without a remainder. We often use factors like organizing events and seating arrangements in our daily lives. In this topic, we will know more about the factors of 374 and the different methods to find them.
What are the Factors of 374?
The factors of 374 are 1, 2, 11, 17, 22, 34, 187, and 374.
Positive Factors: These are numbers greater than 0 that divide 374 completely.
Positive factors: 1, 2, 11, 17, 22, 34, 187, 374
Negative Factors: These are negative counterparts of the positive factors.
Negative factors: -1, -2, -11, -17, -22, -34, -187, -374
Prime Factors: Prime factors are the prime numbers themselves, which when multiplied together give 374 as the product.
Prime factors: 2, 11, 17
Prime Factorization: Prime factorization involves breaking 374 into its prime factors.
It is expressed as 2 × 11 × 17.
Table Listing the Factors of 374
|
Positive Factors |
1, 2, 11, 17, 22, 34, 187, 374 |
|
Negative Factors |
-1, -2, -11, -17, -22, -34, -187, -374 |
|
Prime Factors |
2, 11, 17 |
|
Prime Factorization |
21 × 111 × 171 |
This breakdown helps in understanding the various factors of 374, whether they are positive or negative, as well as how prime factorization works for this number.
How to Find the Factors of 374?
There are different methods to find the factors of 374.
Methods to find the factors of 374:
Multiplication Method
Division Method
Prime Factorization
Factor Tree
Finding Factors Using Multiplication Method
The multiplication method finds the pair of factors that give 374 as their product.
Step 1: Find the pair of numbers whose product is 374.
Step 2: The factors are those numbers that, when multiplied, give 374.
Step 3: Make a list of numbers whose product will be 374.
A list of numbers whose products are 374 is given below:
1 × 374 = 374
2 × 187 = 374
11 × 34 = 374
17 × 22 = 374
Thus, the factors of 374 are 1, 2, 11, 17, 22, 34, 187, and 374.
Finding Factors Using Division Method
The division method finds the numbers that fully divide the given number.
The steps are given below:
Step 1: Since every number is divisible by 1, 1 will always be a factor.
Example: 374 ÷ 1 = 374
Step 2: Move to the next integer. The factors of the number include the divisor and the quotient.
Thus, the factors of 374 are 1, 2, 11, 17, 22, 34, 187, and 374.
Prime Factors and Prime Factorization
Multiplying prime numbers to get the given number as their product is called prime factors. A number when simplified using its factors and expressed in the form of prime factors is the prime factorization of a number.
Prime Factors of 374: Number 374 has three prime factors.
Prime factors of 374: 2, 11, 17
To find the prime factors of 374, we can divide it by the prime numbers 2, 11, and 17 from the list of factors of 374:
Step 1: Divide 374 by the prime number 2.
374 ÷ 2 = 187
Step 2: Divide 187 by the prime number 11.
187 ÷ 11 = 17
Step 3: 17 is a prime number, so it stops here.
Prime Factorization of 374: Prime Factorization breaks down the prime factors of 374:
It is expressed as 21 × 111 × 171
Factor Tree
The prime factorization is visually represented using the factor tree. It helps to understand the process easily.
This tree shows the breakdown of 374 into its prime factors: 2 × 11 × 17.
Positive and Negative Factor Pairs
Factors of 374 can be written in both positive pairs and negative pairs. Their product will be equal to the given number.
Positive Factor Pairs: (1, 374), (2, 187), (11, 34), (17, 22)
Negative Factor Pairs: (-1, -374), (-2, -187), (-11, -34), (-17, -22)
Common Mistakes and How to Avoid Them in Factors of 374
Mistakes can occur while finding the factors. Learn about the common errors and their solutions below:
Mistake 1
Assuming 2 as the only factor of 374.
Remember that factors are numbers that divide the given number completely. Other factors that divide 374 completely are 1, 11, 17, 22, 34, 187, and 374.
Factors of 374 Examples
Problem 1
Can you check whether 374 and 44 are co-prime?
No, 374 and 44 are not co-prime.
Explanation
To check whether two numbers are co-prime, list their factors first.
Once you have listed the factors, identify the common factors and determine the GCF.
If the GCF is greater than 1, then the numbers are not co-prime.
Factors of 374: 1, 2, 11, 22, 17, 34, 187, 374
Factors of 44: 1, 2, 4, 11, 22, 44
Here, the GCF is 22. So 374 and 44 are not co-prime.
For co-prime, the GCF of numbers should be 1.
Problem 2
Verify whether 374 is a multiple of 13
No, 374 is not a multiple of 13.
Explanation
Multiples of 13 are numbers we get when 13 is multiplied by another number. No number can be multiplied by 13 to get 374 as the product.
Problem 3
Identify the perfect square from the factors of 374
There is no perfect square factor of 374
Explanation
A perfect square is a number we get when the same number is multiplied twice. None of the factors of 374 meet this condition.
Problem 4
Can you check whether 374 is divisible by 17?
Yes, 374 is divisible by 17.
Explanation
A number is divisible by another when the quotient is a whole number. Dividing 374 by 17 gives 22, which is a whole number.
Problem 5
Are all factors of 374 even numbers?
No, not all factors of 374 are even numbers
Explanation
Even numbers are divisible by 2. Among the factors of 374, 11 and 17 are odd numbers, so not all factors are even.
FAQs on Factors of 374
1.What are the factors of 374?
2.How do you determine if a number is a factor of 374?
3.What is the smallest factor of 374?
4.What is the largest factor of 374?
5.How many factors does 374 have?
6.How many odd factors does 374 have?
7.What factors go into 374?
8.Do any perfect squares exist in the factors of 374?
Important glossaries for the Factors of 374
- Factors: Numbers that divide another number completely without leaving a remainder. Example: Factors of 374 are 1, 2, 11, 17, 22, 34, 187, and 374.
- Prime Factorization: The process of expressing a number as a product of its prime factors. Example: The prime factorization of 374 is 2×11×17.
- Positive Factors: Factors of a number that are greater than 0. Example: Positive factors of 374 are 1, 2, 11, 17, 22, 34, 187, and 374.
- Negative Factors: Negative counterparts of positive factors that also divide the number completely. Example: Negative factors of 374 are -1, -2, -11, -17, -22, -34, -187, and -374.
- Factor Tree: A diagram that shows the step-by-step prime factorization of a number. Example: The factor tree of 374 breaks it into 2×11×17.
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