118 LearnersLast updated on May 26th, 2025
Factors of 1954
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 1954, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1954?
The numbers that divide 1954 evenly are known as factors of 1954.
A factor of 1954 is a number that divides the number without remainder.
The factors of 1954 are 1, 2, 977, and 1954.
Negative factors of 1954: -1, -2, -977, and -1954.
Prime factors of 1954: 2 and 977.
Prime factorization of 1954: 2 × 977.
The sum of factors of 1954: 1 + 2 + 977 + 1954 = 2934
How to Find Factors of 1954?
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 1954. Identifying the numbers which are multiplied to get the number 1954 is the multiplication method.
Step 1: Multiply 1954 by 1, 1954 × 1 = 1954.
Step 2: Check for other numbers that give 1954 after multiplying 2 × 977 = 1954
Therefore, the positive factor pairs of 1954 are: (1, 1954) and (2, 977).
All these factor pairs result in 1954.
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 1954 by 1, 1954 ÷ 1 = 1954.
Step 2: Continue dividing 1954 by the numbers until the remainder becomes 0.
1954 ÷ 1 = 1954
1954 ÷ 2 = 977
Therefore, the factors of 1954 are: 1, 2, 977, and 1954.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a prime number. 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 1954 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1954 ÷ 2 = 977
977 ÷ 977 = 1
The prime factors of 1954 are 2 and 977.
The prime factorization of 1954 is: 2 × 977.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1954 is divided by 2 to get 977. Here, 977 is a prime number and cannot be divided further. So, the prime factorization of 1954 is: 2 × 977.
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 1954: (1, 1954) and (2, 977).
Negative factor pairs of 1954: (-1, -1954) and (-2, -977).
Common Mistakes and How to Avoid Them in Factors of 1954
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 1954, 1 and 1954 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 1954 consist of -1, -2, -977, 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 1954/1.5 = 1302.666, 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 1954 are prime numbers.
For example, 2 and 977 are the prime factors of 1954, but it has other factors like 1, 1954.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up in writing wrong factors.
For example, not breaking 1954 as 2 × 977 and missing all the key factors.
Factors of 1954 Examples
Problem 1
A farmer has 1954 apples and wants to pack them into boxes of 2 apples each. How many boxes will he need?
He will need 977 boxes.
Explanation
To divide the apples equally into boxes, we need to divide the total apples by the number of apples per box.
1954 ÷ 2 = 977
Problem 2
A conference room is being arranged with 1954 chairs in rows of 2. How many rows will there be?
There will be 977 rows.
Explanation
To find the number of rows, divide the total number of chairs by the number of chairs per row.
1954 ÷ 2 = 977
Problem 3
A library has 1954 books and wants to arrange them in sections of 977 books each. How many sections will there be?
There will be 2 sections.
Explanation
To find the number of sections, divide the total number of books by the number of books per section.
1954 ÷ 977 = 2
Problem 4
A construction project uses 1954 bricks, and each wall requires 977 bricks. How many walls can be constructed?
2 walls can be constructed.
Explanation
To find the number of walls, divide the total number of bricks by the number of bricks per wall.
1954 ÷ 977 = 2
Problem 5
A chef has 1954 grams of flour and wants to use 2 grams per cookie. How many cookies can be made?
977 cookies can be made.
Explanation
To find the number of cookies, divide the total grams of flour by the grams used per cookie.
1954 ÷ 2 = 977
FAQs on Factors of 1954
1.What are the factors of 1954?
2.Mention the prime factors of 1954.
3.Is 1954 a multiple of 2?
4.Mention the factor pairs of 1954?
5.What is the square of 1954?
Important Glossaries for Factors of 1954
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1954 are 1, 2, 977, and 1954.
- Prime factors: The factors which are prime numbers. For example, 2 and 977 are prime factors of 1954.
- 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 1954 are (1, 1954) and (2, 977).
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 1954 is 2 × 977.
- Negative factors: Factors of a number that are negative. For example, the negative factors of 1954 are -1, -2, -977, and -1954.
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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.
