135 LearnersLast updated on May 30th, 2025
Factors of 1216
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of 1216, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1216?
The numbers that divide 1216 evenly are known as factors of 1216.
A factor of 1216 is a number that divides the number without remainder.
The factors of 1216 are 1, 2, 4, 8, 16, 19, 32, 38, 76, 152, 304, 608, and 1216.
Negative factors of 1216: -1, -2, -4, -8, -16, -19, -32, -38, -76, -152, -304, -608, and -1216.
Prime factors of 1216: 2 and 19. Prime factorization of 1216: 24 × 19.
The sum of factors of 1216: 1 + 2 + 4 + 8 + 16 + 19 + 32 + 38 + 76 + 152 + 304 + 608 + 1216 = 2476
How to Find Factors of 1216?
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 1216. Identifying the numbers which are multiplied to get the number 1216 is the multiplication method.
Step 1: Multiply 1216 by 1, 1216 × 1 = 1216.
Step 2: Check for other numbers that give 1216 after multiplying
2 × 608 = 1216
4 × 304 = 1216
8 × 152 = 1216
16 × 76 = 1216
19 × 64 = 1216
Therefore, the positive factor pairs of 1216 are: (1, 1216), (2, 608), (4, 304), (8, 152), (16, 76), (19, 64). All these factor pairs result in 1216. For every 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 1216 by 1, 1216 ÷ 1 = 1216.
Step 2: Continue dividing 1216 by the numbers until the remainder becomes 0.
1216 ÷ 1 = 1216
1216 ÷ 2 = 608
1216 ÷ 4 = 304
1216 ÷ 8 = 152
1216 ÷ 16 = 76
1216 ÷ 19 = 64
Therefore, the factors of 1216 are: 1, 2, 4, 8, 16, 19, 32, 38, 76, 152, 304, 608, 1216.
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 1216 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1216 ÷ 2 = 608
608 ÷ 2 = 304
304 ÷ 2 = 152
152 ÷ 2 = 76
76 ÷ 2 = 38
38 ÷ 2 = 19
19 ÷ 19 = 1
The prime factors of 1216 are 2 and 19.
The prime factorization of 1216 is: 26 × 19.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1216 is divided by 2 to get 608.
Step 2: Now divide 608 by 2 to get 304.
Step 3: Then divide 304 by 2 to get 152.
Step 4: Divide 152 by 2 to get 76.
Step 5: Divide 76 by 2 to get 38.
Step 6: Divide 38 by 2 to get 19. Here, 19 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 1216 is: 26 × 19.
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 1216: (1, 1216), (2, 608), (4, 304), (8, 152), (16, 76), and (19, 64).
Negative factor pairs of 1216: (-1, -1216), (-2, -608), (-4, -304), (-8, -152), (-16, -76), and (-19, -64).
Common Mistakes and How to Avoid Them in Factors of 1216
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 1216, 1 and 1216 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of 1216 consist of -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 1216/1.5 = 810.666, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes. For example, thinking all the factors of 1216 are prime numbers.
For example, 2 and 19 are the prime factors of 1216, but it has other factors like 4, 38.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1216 as 26 × 19 and missing all the key factors.
Factors of 1216 Examples
Problem 1
There are 16 workers and 1216 bricks. How will they divide them equally?
They will get 76 bricks each.
Explanation
To divide the bricks equally, we need to divide the total bricks by the number of workers.
1216/16 = 76
Problem 2
A garden is rectangular, the length of the garden is 19 meters, and the total area is 1216 square meters. Find the width?
64 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width
1216 = 19 × width
To find the value of width, we need to shift 19 to the left side.
1216/19 = width
Width = 64.
Problem 3
There are 32 bags and 1216 apples. How many apples will be in each bag?
Each bag will have 38 apples.
Explanation
To find the apples in each bag, divide the total apples by the bags.
1216/32 = 38
Problem 4
In a class, there are 152 students, and 8 groups. How many students are there in each group?
There are 19 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
152/8 = 19
Problem 5
1216 books need to be arranged in 19 shelves. How many books will go on each shelf?
Each of the shelves has 64 books.
Explanation
Divide total books by shelves.
1216/19 = 64
FAQs on Factors of 1216
1.What are the factors of 1216?
2.Mention the prime factors of 1216.
3.Is 1216 a multiple of 8?
4.Mention the factor pairs of 1216?
5.What is the square of 1216?
6.How can children in India use numbers in everyday life to understand Factors of 1216?
7.What are some fun ways kids in India can practice Factors of 1216 with numbers?
8.What role do numbers and Factors of 1216 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of 1216 skills?
Important Glossaries for Factors of 1216
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1216 are 1, 2, 4, 8, 16, 19, 32, 38, 76, 152, 304, 608, and 1216.
- Prime factors: The factors which are prime numbers. For example, 2 and 19 are prime factors of 1216.
- 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 1216 are (1, 1216), (2, 608), etc.
- Multiplication method: A technique to find factors by identifying pairs of numbers that multiply to give the original number.
- Division method: A technique to find factors by dividing the number by whole numbers to see which ones result in no remainder.
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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.
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