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 460, how they are used in real life, and tips to learn them quickly.
The numbers that divide 460 evenly are known as factors of 460.
A factor of 460 is a number that divides the number without remainder.
The factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, and 460.
Negative factors of 460: -1, -2, -4, -5, -10, -20, -23, -46, -92, -115, -230, and -460.
Prime factors of 460: 2, 5, and 23.
Prime factorization of 460: 2 × 2 × 5 × 23.
The sum of factors of 460: 1 + 2 + 4 + 5 + 10 + 20 + 23 + 46 + 92 + 115 + 230 + 460 = 1008
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 460. Identifying the numbers that are multiplied to get the number 460 is the multiplication method.
Step 1: Multiply 460 by 1, 460 × 1 = 460.
Step 2: Check for other numbers that give 460 after multiplying
2 × 230 = 460
4 × 115 = 460
5 × 92 = 460
10 × 46 = 460
20 × 23 = 460
Therefore, the positive factor pairs of 460 are: (1, 460), (2, 230), (4, 115), (5, 92), (10, 46), (20, 23).
For every positive factor, there is a negative factor.
Dividing the given numbers with whole numbers until the remainder becomes zero and listing out the numbers that result as whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 460 by 1, 460 ÷ 1 = 460.
Step 2: Continue dividing 460 by the numbers until the remainder becomes 0.
460 ÷ 1 = 460
460 ÷ 2 = 230
460 ÷ 4 = 115
460 ÷ 5 = 92
460 ÷ 10 = 46
460 ÷ 20 = 23
Therefore, the factors of 460 are: 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460.
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 460 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
460 ÷ 2 = 230
230 ÷ 2 = 115
115 ÷ 5 = 23
23 ÷ 23 = 1
The prime factors of 460 are 2, 5, and 23.
The prime factorization of 460 is: 2 × 2 × 5 × 23.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 460 is divided by 2 to get 230.
Step 2: Now divide 230 by 2 to get 115.
Step 3: Then divide 115 by 5 to get 23.
Step 4: Here, 23 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 460 is: 2 × 2 × 5 × 23.
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 460: (1, 460), (2, 230), (4, 115), (5, 92), (10, 46), (20, 23).
Negative factor pairs of 460: (-1, -460), (-2, -230), (-4, -115), (-5, -92), (-10, -46), (-20, -23).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 23 students and 460 pencils. How will they divide it equally?
They will get 20 pencils each.
To divide the pencils equally, we need to divide the total pencils with the number of students.
460/23 = 20
A field is rectangular, the length of the field is 23 meters and the total area is 460 square meters. Find the width?
20 meters.
To find the width of the field, we use the formula,
Area = length × width
460 = 23 × width
To find the value of width, we need to shift 23 to the left side.
460/23 = width
Width = 20.
There are 10 boxes and 460 marbles. How many marbles will be in each box?
Each box will have 46 marbles.
To find the marbles in each box, divide the total marbles with the boxes.
460/10 = 46
In a class, there are 460 students, and 20 groups. How many students are there in each group?
There are 23 students in each group.
Dividing the students with the total groups, we will get the number of students in each group.
460/20 = 23
460 books need to be arranged in 5 shelves. How many books will go on each shelf?
Each of the shelves has 92 books.
Divide total books with shelves.
460/5 = 92
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.