Last updated on May 26th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
A teacher wants to split 51 candies among 3 students equally. How many candies will each student get?
Each student will get 17 candies.
To divide the candies equally, we need to divide the total candies with the number of students.
51/3 = 17
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.
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.
There are 51 apples and 17 baskets. How many apples will be in each basket?
Each basket will have 3 apples.
To find the apples in each basket, divide the total apples with the baskets.
51/17 = 3
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.
Dividing the chairs with the total rows, we will get the number of chairs in each row.
51/3 = 17
51 books need to be arranged in 3 shelves. How many books will go on each shelf?
Each of the shelves has 17 books.
Divide total books with shelves.
51/3 = 17
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.
: She loves to read number jokes and games.