124 LearnersLast updated on May 26th, 2025
Factors of -51
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 -51, how they are used in real life, and the tips to learn them quickly.
What are the Factors of -51?
The numbers that divide -51 evenly are known as factors of -51.
A factor of -51 is a number that divides the number without remainder.
The factors of -51 are 1, 3, 17, and 51.
Negative factors of -51: -1, -3, -17, and -51.
Prime factors of -51: 3 and 17.
Prime factorization of -51: -1 × 3 × 17.
The sum of factors of -51: 1 + 3 + 17 + 51 = 72
How to Find Factors of -51?
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 -51. Identifying the numbers which are multiplied to get the number -51 is the multiplication method.
Step 1: Multiply -51 by -1, -51 × -1 = 51.
Step 2: Check for other numbers that give 51 after multiplying 3 × 17 = 51
Therefore, the positive factor pairs of -51 are: (1, 51), (3, 17).
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 51 by 1, 51 ÷ 1 = 51.
Step 2: Continue dividing 51 by the numbers until the remainder becomes 0.
51 ÷ 1 = 51
51 ÷ 3 = 17
51 ÷ 17 = 3
51 ÷ 51 = 1
Therefore, the factors of -51 are: 1, 3, 17, 51.
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 51 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
51 ÷ 3 = 17
17 ÷ 17 = 1
The prime factors of -51 are 3 and 17.
The prime factorization of -51 is: -1 × 3 × 17.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 51 is divided by 3 to get 17.
Step 2: Now divide 17 by 17 to get 1. So, the prime factors of -51 are 3 and 17.
The prime factorization of -51 is: -1 × 3 × 17.
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 -51: (1, 51), (3, 17).
Negative factor pairs of -51: (-1, -51), (-3, -17).
Common Mistakes and How to Avoid Them in Factors of -51
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 -51, 1 and 51 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 -51 consist of -1, -3, -17, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 51/1.5 = 34, 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 -51 are prime numbers.
For example, 3 and 17 are the prime factors of -51, but it has other factors like 51.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 51 as -1 × 3 × 17 and missing all the key factors.
Factors of -51 Examples
Problem 1
A teacher wants to split 51 candies among 3 students equally. How many candies will each student get?
Each student will get 17 candies.
Explanation
To divide the candies equally, we need to divide the total candies with the number of students.
51/3 = 17
Problem 2
A rectangular garden has a length of 17 meters and a total area of 51 square meters. What is the width of the garden?
3 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width
51 = 17 × width
To find the value of width, we need to shift 17 to the left side.
51/17 = width
Width = 3.
Problem 3
There are 51 apples and 17 baskets. How many apples will be in each basket?
Each basket will have 3 apples.
Explanation
To find the apples in each basket, divide the total apples with the baskets.
51/17 = 3
Problem 4
A classroom has 51 chairs, and there are 3 rows. How many chairs are there in each row?
There are 17 chairs in each row.
Explanation
Dividing the chairs with the total rows, we will get the number of chairs in each row.
51/3 = 17
Problem 5
51 books need to be arranged in 3 shelves. How many books will go on each shelf?
Each of the shelves has 17 books.
Explanation
Divide total books with shelves.
51/3 = 17
FAQs on Factors of -51
1.What are the factors of -51?
2.Mention the prime factors of -51.
3.Is 51 a multiple of 3?
4.Mention the factor pairs of -51?
5.What is the square of 51?
6.How can children in Oman use numbers in everyday life to understand Factors of -51?
7.What are some fun ways kids in Oman can practice Factors of -51 with numbers?
8.What role do numbers and Factors of -51 play in helping children in Oman develop problem-solving skills?
9.How can families in Oman create number-rich environments to improve Factors of -51 skills?
Important Glossaries for Factors of -51
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -51 are 1, 3, 17, and 51.
- Prime factors: The factors which are prime numbers. For example, 3 and 17 are prime factors of -51.
- 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 -51 are (1, 51), (3, 17), etc.
- Negative factors: The negative counterparts of the positive factors. For example, -1, -3, -17, -51 for -51.
- Multiplication method: A technique to find factors by identifying pairs of numbers that multiply to give the original number.
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About BrightChamps in Oman
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.
