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 1408, how they are used in real life, and the tips to learn them quickly.
The numbers that divide 1408 evenly are known as factors of 1408.
A factor of 1408 is a number that divides the number without remainder.
The factors of 1408 are 1, 2, 4, 8, 16, 32, 44, 88, 176, 352, 704, and 1408.
Negative factors of 1408: -1, -2, -4, -8, -16, -32, -44, -88, -176, -352, -704, and -1408.
Prime factors of 1408: 2 and 11.
Prime factorization of 1408: 26 × 11.
The sum of factors of 1408: 1 + 2 + 4 + 8 + 16 + 32 + 44 + 88 + 176 + 352 + 704 + 1408 = 2835
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 1408. Identifying the numbers which are multiplied to get the number 1408 is the multiplication method.
Step 1: Multiply 1408 by 1, 1408 × 1 = 1408.
Step 2: Check for other numbers that give 1408 after multiplying
2 × 704 = 1408
4 × 352 = 1408
8 × 176 = 1408
16 × 88 = 1408
32 × 44 = 1408
Therefore, the positive factor pairs of 1408 are: (1, 1408), (2, 704), (4, 352), (8, 176), (16, 88), (32, 44).
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 1408 by 1, 1408 ÷ 1 = 1408.
Step 2: Continue dividing 1408 by the numbers until the remainder becomes 0.
1408 ÷ 1 = 1408
1408 ÷ 2 = 704
1408 ÷ 4 = 352
1408 ÷ 8 = 176
1408 ÷ 16 = 88
1408 ÷ 32 = 44
Therefore, the factors of 1408 are: 1, 2, 4, 8, 16, 32, 44, 88, 176, 352, 704, 1408.
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 1408 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1408 ÷ 2 = 704
704 ÷ 2 = 352
352 ÷ 2 = 176
176 ÷ 2 = 88
88 ÷ 2 = 44
44 ÷ 2 = 22
22 ÷ 2 = 11
11 ÷ 11 = 1
The prime factors of 1408 are 2 and 11. The prime factorization of 1408 is: 26 × 11.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1408 is divided by 2 to get 704.
Step 2: Now divide 704 by 2 to get 352.
Step 3: Then divide 352 by 2 to get 176.
Step 4: Continue dividing by 2 until you get 11.
Step 5: Finally divide 11 by 11 to get 1. Here, 11 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 1408 is: 26 × 11.
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 1408: (1, 1408), (2, 704), (4, 352), (8, 176), (16, 88), and (32, 44).
Negative factor pairs of 1408: (-1, -1408), (-2, -704), (-4, -352), (-8, -176), (-16, -88), and (-32, -44).
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 16 friends and 1408 candies. How will they divide it equally?
They will get 88 candies each.
To divide the candies equally, we need to divide the total candies by the number of friends.
1408/16 = 88
A field is rectangular, and the length of the field is 88 meters. The total area is 1408 square meters. Find the width.
16 meters.
To find the width of the field, we use the formula,
Area = length × width
1408 = 88 × width
To find the value of width, we need to shift 88 to the left side.
1408/88 = width
Width = 16.
There are 32 bags and 1408 apples. How many apples will be in each bag?
Each bag will have 44 apples.
To find the apples in each bag, divide the total apples by the bags.
1408/32 = 44
In a school, there are 1408 students, and 44 classes. How many students are there in each class?
There are 32 students in each class.
Dividing the students by the total classes, we will get the number of students in each class.
1408/44 = 32
1408 books need to be arranged in 88 shelves. How many books will go on each shelf?
Each of the shelves has 16 books.
Divide total books by shelves.
1408/88 = 16
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.