137 LearnersLast updated on May 26th, 2025
Factors of 1416
Factors are the numbers that divide any given number evenly without a 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 1416, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1416?
The numbers that divide 1416 evenly are known as factors of 1416.
A factor of 1416 is a number that divides the number without a remainder.
The factors of 1416 are 1, 2, 3, 4, 6, 8, 12, 24, 59, 118, 177, 236, 354, 472, 708, and 1416.
Negative factors of 1416: -1, -2, -3, -4, -6, -8, -12, -24, -59, -118, -177, -236, -354, -472, -708, and -1416.
Prime factors of 1416: 2, 3, and 59.
Prime factorization of 1416: 2³ × 3 × 59.
The sum of factors of 1416: 1 + 2 + 3 + 4 + 6 + 8 + 12 + 24 + 59 + 118 + 177 + 236 + 354 + 472 + 708 + 1416 = 3600
How to Find Factors of 1416?
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 1416. Identifying the numbers which are multiplied to get the number 1416 is the multiplication method.
Step 1: Multiply 1416 by 1, 1416 × 1 = 1416.
Step 2: Check for other numbers that give 1416 after multiplying
2 × 708 = 1416
3 × 472 = 1416
4 × 354 = 1416
6 × 236 = 1416
8 × 177 = 1416
12 × 118 = 1416
24 × 59 = 1416
Therefore, the positive factor pairs of 1416 are: (1, 1416), (2, 708), (3, 472), (4, 354), (6, 236), (8, 177), (12, 118), (24, 59).
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 which result as whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 1416 by 1, 1416 ÷ 1 = 1416.
Step 2: Continue dividing 1416 by the numbers until the remainder becomes 0.
1416 ÷ 1 = 1416
1416 ÷ 2 = 708
1416 ÷ 3 = 472
1416 ÷ 4 = 354
1416 ÷ 6 = 236
1416 ÷ 8 = 177
1416 ÷ 12 = 118
1416 ÷ 24 = 59
Therefore, the factors of 1416 are: 1, 2, 3, 4, 6, 8, 12, 24, 59, 118, 177, 236, 354, 472, 708, 1416.
Prime Factors and Prime Factorization
The factors can be found by dividing it 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 1416 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1416 ÷ 2 = 708
708 ÷ 2 = 354
354 ÷ 2 = 177
177 ÷ 3 = 59
59 ÷ 59 = 1
The prime factors of 1416 are 2, 3, and 59.
The prime factorization of 1416 is: 2³ × 3 × 59.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1416 is divided by 2 to get 708.
Step 2: Now divide 708 by 2 to get 354.
Step 3: Then divide 354 by 2 to get 177.
Step 4: Divide 177 by 3 to get 59. Here, 59 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 1416 is: 2³ × 3 × 59.
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 1416: (1, 1416), (2, 708), (3, 472), (4, 354), (6, 236), (8, 177), (12, 118), (24, 59).
Negative factor pairs of 1416: (-1, -1416), (-2, -708), (-3, -472), (-4, -354), (-6, -236), (-8, -177), (-12, -118), (-24, -59).
Common Mistakes and How to Avoid Them in Factors of 1416
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 word. Always remember to include 1 and the number itself.
For example, in factors of 1416, 1 and 1416 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 1416 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1416/1.5 = 944, 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 1416 are prime numbers.
For example, 2, 3, and 59 are the prime factors of 1416, but it has other factors like 4, 6.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1416 as 2³ × 3 × 59 and missing all the key factors.
Factors of 1416 Examples
Problem 1
There are 12 boxes and 1416 apples. How will they divide it equally?
They will get 118 apples each.
Explanation
To divide the apples equally, we need to divide the total apples by the number of boxes.
1416/12 = 118
Problem 2
A garden is rectangular, the length of the garden is 59 meters, and the total area is 1416 square meters. Find the width?
24 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1416 = 59 × width
To find the value of width, we need to shift 59 to the left side.
1416/59 = width
Width = 24.
Problem 3
There are 4 crates and 1416 oranges. How many oranges will be in each crate?
Each crate will have 354 oranges.
Explanation
To find the oranges in each crate, divide the total oranges by the crates.
1416/4 = 354
Problem 4
In a theater, there are 236 seats, and the show runs 6 times. How many people can attend each show?
There are 236 people attending each show.
Explanation
Dividing the total seats by the number of shows, we will get the number of people in each show.
1416/6 = 236
Problem 5
1416 liters of water need to be stored in 8 tanks. How many liters will go in each tank?
Each of the tanks has 177 liters.
Explanation
Divide the total liters by the number of tanks.
1416/8 = 177
FAQs on Factors of 1416
1.What are the factors of 1416?
2.Mention the prime factors of 1416.
3.Is 1416 a multiple of 4?
4.Mention the factor pairs of 1416?
5.What is the square of 1416?
6.How can children in Canada use numbers in everyday life to understand Factors of 1416?
7.What are some fun ways kids in Canada can practice Factors of 1416 with numbers?
8.What role do numbers and Factors of 1416 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 1416 skills?
Important Glossaries for Factor of 1416
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1416 are 1, 2, 3, 4, 6, 8, 12, 24, 59, 118, 177, 236, 354, 472, 708, and 1416.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 59 are prime factors of 1416.
- 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 1416 are (1, 1416), (2, 708), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 1416 is 2³ × 3 × 59.
- Divisors: Another term for factors, the numbers that divide the original number evenly. For example, the divisors of 1416 are the same as its factors.
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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
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