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 354, how they are used in real life, and tips to learn them quickly.
The numbers that divide 354 evenly are known as factors of 354.
A factor of 354 is a number that divides the number without remainder.
The factors of 354 are 1, 2, 3, 6, 59, 118, 177, and 354.
Negative factors of 354: -1, -2, -3, -6, -59, -118, -177, and -354. Prime factors of 354: 2, 3, and 59.
Prime factorization of 354: 2 × 3 × 59.
The sum of factors of 354: 1 + 2 + 3 + 6 + 59 + 118 + 177 + 354 = 720
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 354. Identifying the numbers which are multiplied to get the number 354 is the multiplication method.
Step 1: Multiply 354 by 1, 354 × 1 = 354.
Step 2: Check for other numbers that give 354 after multiplying 2 × 177 = 354 3 × 118 = 354 6 × 59 = 354
Therefore, the positive factor pairs of 354 are: (1, 354), (2, 177), (3, 118), (6, 59).
All these factor pairs result in 354.
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 354 by 1, 354 ÷ 1 = 354.
Step 2: Continue dividing 354 by the numbers until the remainder becomes 0.
354 ÷ 1 = 354
354 ÷ 2 = 177
354 ÷ 3 = 118
354 ÷ 6 = 59
Therefore, the factors of 354 are: 1, 2, 3, 6, 59, 118, 177, 354.
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 354 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
354 ÷ 2 = 177
177 ÷ 3 = 59
59 ÷ 59 = 1
The prime factors of 354 are 2, 3, and 59.
The prime factorization of 354 is: 2 × 3 × 59.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 354 is divided by 2 to get 177.
Step 2: Now divide 177 by 3 to get 59.
Step 3: Divide 59 by 59 to get 1. Here, 59 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 354 is: 2 × 3 × 59.
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 354: (1, 354), (2, 177), (3, 118), and (6, 59).
Negative factor pairs of 354: (-1, -354), (-2, -177), (-3, -118), and (-6, -59).
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 6 teams and 354 players. How will they divide them equally?
They will get 59 players each.
To divide the players equally, we need to divide the total players with the number of teams.
354/6 = 59
A garden is rectangular, the length of the garden is 59 meters, and the total area is 354 square meters. Find the width?
6 meters.
To find the width of the garden, we use the formula,
Area = length × width
354 = 59 × width
To find the value of width, we need to shift 59 to the left side.
354/59 = width
Width = 6.
There are 3 boxes and 354 candies. How many candies will be in each box?
Each box will have 118 candies.
To find the candies in each box, divide the total candies with the boxes.
354/3 = 118
In a class, there are 354 students, and 2 sections. How many students are there in each section?
There are 177 students in each section.
Dividing the students with the total sections, we will get the number of students in each section.
354/2 = 177
354 plants need to be arranged in 59 rows. How many plants will go in each row?
Each of the rows has 6 plants.
Divide total plants with rows.
354/59 = 6
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.