109 LearnersLast updated on May 26th, 2025
Factors of 1272
Factors are the numbers that divide any given number evenly without a remainder. In daily life, we use factors for tasks such as sharing items equally, arranging things, etc. In this topic, we will learn about the factors of 1272, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1272?
The numbers that divide 1272 evenly are known as factors of 1272. A factor of 1272 is a number that divides the number without a remainder. The factors of 1272 are 1, 2, 3, 4, 6, 12, 53, 106, 159, 212, 318, 636, and 1272.
Negative factors of 1272: -1, -2, -3, -4, -6, -12, -53, -106, -159, -212, -318, -636, and -1272.
Prime factors of 1272: 2, 3, and 53.
Prime factorization of 1272: 22 × 3 × 53.
The sum of factors of 1272: 1 + 2 + 3 + 4 + 6 + 12 + 53 + 106 + 159 + 212 + 318 + 636 + 1272 = 2784
How to Find Factors of 1272?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the 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 1272. Identifying the numbers which are multiplied to get the number 1272 is the multiplication method.
Step 1: Multiply 1272 by 1, 1272 × 1 = 1272.
Step 2: Check for other numbers that give 1272 after multiplying
2 × 636 = 1272
3 × 424 = 1272
4 × 318 = 1272
6 × 212 = 1272
12 × 106 = 1272
53 × 24 = 1272
Therefore, the positive factor pairs of 1272 are: (1, 1272), (2, 636), (3, 424), (4, 318), (6, 212), (12, 106), and (53, 24). For each positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 1272 by 1, 1272 ÷ 1 = 1272.
Step 2: Continue dividing 1272 by the numbers until the remainder becomes 0.
1272 ÷ 1 = 1272
1272 ÷ 2 = 636
1272 ÷ 3 = 424
1272 ÷ 4 = 318
1272 ÷ 6 = 212
1272 ÷ 12 = 106
1272 ÷ 53 = 24
Therefore, the factors of 1272 are: 1, 2, 3, 4, 6, 12, 53, 106, 159, 212, 318, 636, and 1272.
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 1272 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1272 ÷ 2 = 636
636 ÷ 2 = 318
318 ÷ 3 = 106
106 ÷ 53 = 2
2 ÷ 1 = 0
The prime factors of 1272 are 2, 3, and 53. The prime factorization of 1272 is: 22 × 3 × 53.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1272 is divided by 2 to get 636.
Step 2: Now divide 636 by 2 to get 318.
Step 3: Then divide 318 by 3 to get 106.
Step 4: Divide 106 by 53 to get 2. Here, 53 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1272 is: 22 × 3 × 53.
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 1272: (1, 1272), (2, 636), (3, 424), (4, 318), (6, 212), (12, 106), and (53, 24).
- Negative factor pairs of 1272: (-1, -1272), (-2, -636), (-3, -424), (-4, -318), (-6, -212), (-12, -106), and (-53, -24).
Common Mistakes and How to Avoid Them in Factors of 1272
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 number. Always remember to include 1 and the number itself. For example, in factors of 1272, 1 and 1272 are also factors.
Factors of 1272 Examples
Problem 1
A group of 6 friends plans a road trip and needs to split 1272 miles equally among them. How many miles will each friend drive?
Each friend will drive 212 miles.
Explanation
To divide the miles equally, we need to divide the total miles by the number of friends.
1272/6 = 212
Problem 2
A rectangular garden has an area of 1272 square meters and a width of 53 meters. Find the length of the garden.
24 meters.
Explanation
To find the length of the garden, we use the formula,
Area = length × width
1272 = length × 53
To find the value of length, we need to shift 53 to the left side.
1272/53 = length
Length = 24.
Problem 3
A company wants to distribute 1272 promotional items evenly across 4 regions. How many items will each region receive?
Each region will receive 318 items.
Explanation
To find the items each region will receive, divide the total items by the number of regions.
1272/4 = 318
Problem 4
A school has 1272 students, and they are divided into 318 groups for an event. How many students are in each group?
There are 4 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
1272/318 = 4
Problem 5
1272 books need to be arranged in 53 shelves. How many books will go on each shelf?
Each of the shelves has 24 books.
Explanation
Divide the total books by the shelves.
1272/53 = 24
FAQs on Factors of 1272
1.What are the factors of 1272?
2.Mention the prime factors of 1272.
3.Is 1272 a multiple of 4?
4.Mention the factor pairs of 1272.
5.What is the square of 1272?
Important Glossaries for Factor of 1272
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1272 are 1, 2, 3, 4, 6, 12, 53, 106, 159, 212, 318, 636, and 1272.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 53 are prime factors of 1272.
- 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 1272 are (1, 1272), (2, 636), etc.
- Prime factorization: The process of expressing a number as a product of its prime factors. For 1272, it is 22 × 3 × 53.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 1272 is a multiple of 4.
Explore More numbers
Previous to Factors of 1272
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.
