101 LearnersLast updated on May 26th, 2025
Factors of 1274
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of 1274, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1274?
The numbers that divide 1274 evenly are known as factors of 1274.
A factor of 1274 is a number that divides the number without remainder.
The factors of 1274 are 1, 2, 3, 6, 7, 14, 21, 42, 29, 58, 87, 174, 203, 406, 609, and 1274.
Negative factors of 1274: -1, -2, -3, -6, -7, -14, -21, -42, -29, -58, -87, -174, -203, -406, -609, and -1274.
Prime factors of 1274: 2, 3, 7, and 29.
Prime factorization of 1274: 2 × 3 × 7 × 29.
The sum of factors of 1274: 1 + 2 + 3 + 6 + 7 + 14 + 21 + 42 + 29 + 58 + 87 + 174 + 203 + 406 + 609 + 1274 = 2936
How to Find Factors of 1274?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using division method
- Prime factors and Prime factorization
Finding Factors Using Multiplication
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 1274. Identifying the numbers that are multiplied to get the number 1274 is the multiplication method.
Step 1: Multiply 1274 by 1, 1274 × 1 = 1274.
Step 2: Check for other numbers that give 1274 after multiplying
2 × 637 = 1274
3 × 424.67 (Not a factor)
6 × 212.33 (Not a factor)
7 × 182 = 1274
14 × 91 = 1274
21 × 60.67 (Not a factor)
42 × 30.33 (Not a factor)
29 × 44 = 1274
Therefore, the positive factor pairs of 1274 are: (1, 1274), (2, 637), (7, 182), (14, 91), and (29, 44).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers that result in whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 1274 by 1, 1274 ÷ 1 = 1274.
Step 2: Continue dividing 1274 by the numbers until the remainder becomes 0.
1274 ÷ 1 = 1274
1274 ÷ 2 = 637
1274 ÷ 3 = 424.67 (Not a factor)
1274 ÷ 6 = 212.33 (Not a factor)
1274 ÷ 7 = 182
1274 ÷ 14 = 91
1274 ÷ 29 = 44
Therefore, the factors of 1274 are: 1, 2, 7, 14, 29, 44, 91, 182, 637, and 1274.
Prime Factors and Prime Factorization
The factors can be found by dividing them with prime numbers. We can find the prime factors using the following methods:
- Using prime factorization
- Using factor tree
Using Prime Factorization: In this process, prime factors of 1274 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1274 ÷ 2 = 637
637 ÷ 3 = 212.33 (Not a factor)
637 ÷ 7 = 91
91 ÷ 7 = 13
13 ÷ 13 = 1
The prime factors of 1274 are 2, 3, 7, and 29.
The prime factorization of 1274 is: 2 × 3 × 7 × 29.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show -
Step 1: Firstly, 1274 is divided by 2 to get 637.
Step 2: 637 is not divisible by 3, so divide 637 by 7 to get 91.
Step 3: Now divide 91 by 7 to get 13.
Step 4: Divide 13 by 13 to get 1.
So, the prime factorization of 1274 is: 2 × 3 × 7 × 29.
Factor Pairs Two numbers that are multiplied to give a specific number are called factor pairs.
Both positive and negative factors constitute factor pairs.
Positive factor pairs of 1274: (1, 1274), (2, 637), (7, 182), (14, 91), and (29, 44).
Negative factor pairs of 1274: (-1, -1274), (-2, -637), (-7, -182), (-14, -91), and (-29, -44).
Common Mistakes and How to Avoid Them in Factors of 1274
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
Mistake 1
Forgetting the number itself and 1 is a factor
Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are the factors for every whole number. Always remember to include 1 and the number itself.
For example, in factors of 1274, 1 and 1274 are also factors.
Factors of 1274 Examples
Problem 1
There are 7 teams and 1274 medals. How will they distribute them equally?
They will get 182 medals each.
Explanation
To distribute the medals equally, we need to divide the total medals with the number of teams.
1274/7 = 182
Problem 2
A garden is rectangular, the length of the garden is 14 meters and the total area is 1274 square meters. Find the width?
91 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1274 = 14 × width
To find the value of width, we need to shift 14 to the left side.
1274/14 = width
Width = 91.
Problem 3
There are 14 crates and 1274 apples. How many apples will be in each crate?
Each crate will have 91 apples.
Explanation
To find the apples in each crate, divide the total apples with the crates.
1274/14 = 91
Problem 4
In a school, there are 203 students, and 1274 books. How many books are there for each student?
There are 6 books for each student.
Explanation
Dividing the books with the total students, we will get the number of books for each student.
1274/203 = 6
Problem 5
1274 chairs need to be arranged in 29 rows. How many chairs will go in each row?
Each of the rows has 44 chairs.
Explanation
Divide total chairs with rows.
1274/29 = 44
FAQs on Factors of 1274
1.What are the factors of 1274?
2.Mention the prime factors of 1274.
3.Is 1274 a multiple of 7?
4.Mention the factor pairs of 1274?
5.What is the square of 1274?
Important Glossaries for Factor of 1274
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1274 are 1, 2, 3, 6, 7, 14, 21, 42, 29, 58, 87, 174, 203, 406, 609, and 1274.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 7, and 29 are prime factors of 1274.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 1274 are (1, 1274), (2, 637), etc.
- Prime factorization: The representation of a number as a product of its prime factors. For example, the prime factorization of 1274 is 2 × 3 × 7 × 29.
- Multiplication method: A method to find factors by identifying number pairs that multiply to the given number. For example, using multiplication to find factors of 1274.
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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.
