117 LearnersLast updated on May 26th, 2025
Factors of 1972
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 1972, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1972?
The numbers that divide 1972 evenly are known as factors of 1972.
A factor of 1972 is a number that divides the number without remainder.
The factors of 1972 are 1, 2, 4, 7, 14, 28, 71, 142, 284, 493, 986, and 1972.
Negative factors of 1972: -1, -2, -4, -7, -14, -28, -71, -142, -284, -493, -986, and -1972.
Prime factors of 1972: 2, 7, and 71.
Prime factorization of 1972: 2² × 7 × 71.
The sum of factors of 1972: 1 + 2 + 4 + 7 + 14 + 28 + 71 + 142 + 284 + 493 + 986 + 1972 = 4004
How to Find Factors of 1972?
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 1972. Identifying the numbers which are multiplied to get the number 1972 is the multiplication method.
Step 1: Multiply 1972 by 1, 1972 × 1 = 1972.
Step 2: Check for other numbers that give 1972 after multiplying
2 × 986 = 1972
4 × 493 = 1972
7 × 284 = 1972
14 × 142 = 1972
28 × 71 = 1972
Therefore, the positive factor pairs of 1972 are: (1, 1972), (2, 986), (4, 493), (7, 284), (14, 142), (28, 71).
All these factor pairs result in 1972.
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 1972 by 1, 1972 ÷ 1 = 1972.
Step 2: Continue dividing 1972 by the numbers until the remainder becomes 0.
1972 ÷ 1 = 1972
1972 ÷ 2 = 986
1972 ÷ 4 = 493
1972 ÷ 7 = 284
1972 ÷ 14 = 142
1972 ÷ 28 = 71
Therefore, the factors of 1972 are: 1, 2, 4, 7, 14, 28, 71, 142, 284, 493, 986, 1972.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a 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 1972 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1972 ÷ 2 = 986
986 ÷ 2 = 493
493 ÷ 7 = 71
71 ÷ 71 = 1
The prime factors of 1972 are 2, 7, and 71.
The prime factorization of 1972 is: 2² × 7 × 71.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1972 is divided by 2 to get 986.
Step 2: Now divide 986 by 2 to get 493.
Step 3: Then divide 493 by 7 to get 71. Here, 71 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1972 is: 2² × 7 × 71.
Factor Pairs Two numbers that are multiplied to give a specific number are called as factor pairs.
Both positive and negative factors constitute factor pairs.
Positive factor pairs of 1972: (1, 1972), (2, 986), (4, 493), (7, 284), (14, 142), (28, 71).
Negative factor pairs of 1972: (-1, -1972), (-2, -986), (-4, -493), (-7, -284), (-14, -142), (-28, -71).
Common Mistakes and How to Avoid Them in Factors of 1972
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 1972, 1 and 1972 is also a factor.
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 1972 consist of -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a fraction. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1972/1.5 = 1314.666, 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 1972 are prime numbers.
For example, 2, 7, and 71 are the prime factors of 1972, but it has other factors like 4, 142.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up in writing wrong factors.
For example, not breaking 1972 as 2² × 7 × 71 and missing all the key factors.
Factors of 1972 Examples
Problem 1
There are 4 teams and 1972 participants. How will they be divided equally?
Each team will have 493 participants.
Explanation
To divide the participants equally, we need to divide the total participants by the number of teams.
1972/4 = 493
Problem 2
A garden has a rectangular shape with a length of 14 meters and a total area of 1972 square meters. Find the width.
141 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1972 = 14 × width
To find the value of width, we need to shift 14 to the left side.
1972/14 = width
Width = 141.
Problem 3
There are 28 crates and 1972 apples. How many apples will be in each crate?
Each crate will have 71 apples.
Explanation
To find the apples in each crate, divide the total apples by the number of crates.
1972/28 = 71
Problem 4
In an auditorium, there are 1972 seats and 7 sections. How many seats are there in each section?
There are 284 seats in each section.
Explanation
Dividing the total seats by the number of sections, we will get the number of seats in each section.
1972/7 = 284
Problem 5
A library has 1972 books and 142 shelves. How many books will go on each shelf?
Each of the shelves has 14 books.
Explanation
Divide the total books by the number of shelves.
1972/142 = 14
FAQs on Factors of 1972
1.What are the factors of 1972?
2.Mention the prime factors of 1972.
3.Is 1972 a multiple of 4?
4.Mention the factor pairs of 1972?
5.What is the square of 1972?
6.How can children in Vietnam use numbers in everyday life to understand Factors of 1972?
7.What are some fun ways kids in Vietnam can practice Factors of 1972 with numbers?
8.What role do numbers and Factors of 1972 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve Factors of 1972 skills?
Important Glossaries for Factor of 1972
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1972 are 1, 2, 4, 7, 14, 28, 71, 142, 284, 493, 986, and 1972.
- Prime factors: The factors which are prime numbers. For example, 2, 7, and 71 are prime factors of 1972.
- 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 1972 are (1, 1972), (2, 986), etc.
- Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 1972 is 2² × 7 × 71.
- Multiple: A number that can be divided by another number without a remainder. For example, 1972 is a multiple of 4.
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About BrightChamps in Vietnam
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.
