102 LearnersLast updated on May 26th, 2025
Factors of 742
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of 742, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 742?
The numbers that divide 742 evenly are known as factors of 742.
A factor of 742 is a number that divides the number without remainder.
The factors of 742 are 1, 2, 7, 53, 106, 371, and 742.
Negative factors of 742: -1, -2, -7, -53, -106, -371, and -742.
Prime factors of 742: 2, 7, and 53.
Prime factorization of 742: 2 × 7 × 53.
The sum of factors of 742: 1 + 2 + 7 + 53 + 106 + 371 + 742 = 1282
How to Find Factors of 742?
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 742. Identifying the numbers which are multiplied to get the number 742 is the multiplication method.
Step 1: Multiply 742 by 1, 742 × 1 = 742.
Step 2: Check for other numbers that give 742 after multiplying
2 × 371 = 742
7 × 106 = 742
53 × 14 = 742
Therefore, the positive factor pairs of 742 are: (1, 742), (2, 371), (7, 106), (14, 53).
All these factor pairs result in 742.
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 742 by 1, 742 ÷ 1 = 742.
Step 2: Continue dividing 742 by the numbers until the remainder becomes 0.
742 ÷ 1 = 742
742 ÷ 2 = 371
742 ÷ 7 = 106
742 ÷ 53 = 14
Therefore, the factors of 742 are: 1, 2, 7, 53, 106, 371, 742.
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 742 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
742 ÷ 2 = 371
371 ÷ 7 = 53
53 ÷ 53 = 1
The prime factors of 742 are 2, 7, and 53.
The prime factorization of 742 is: 2 × 7 × 53.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 742 is divided by 2 to get 371.
Step 2: Now divide 371 by 7 to get 53.
Step 3: Divide 53 by itself to get 1. Here, 53 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 742 is: 2 × 7 × 53.
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 742: (1, 742), (2, 371), (7, 106), (14, 53).
Negative factor pairs of 742: (-1, -742), (-2, -371), (-7, -106), (-14, -53).
Common Mistakes and How to Avoid Them in Factors of 742
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 742, 1 and 742 are also factors.
Factors of 742 Examples
Problem 1
There are 742 pages in a book, and 2 people want to distribute them equally. How many pages will each person get?
Each person will get 371 pages.
Explanation
To divide the pages equally, we need to divide the total pages with the number of people.
742/2 = 371
Problem 2
A garden is rectangular, the length of the garden is 53 meters, and the total area is 742 square meters. Find the width.
14 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width 742 = 53 × width
To find the value of width, we need to shift 53 to the left side.
742/53 = width
Width = 14.
Problem 3
There are 371 candies and 742 people. How many candies will be in each person's share if each person gets the same amount?
Each person will get 2 candies.
Explanation
To find the candies in each person's share, divide the total candies by the people.
742/371 = 2
Problem 4
A class has 742 students, and they need to be divided into 53 groups. How many students will be there in each group?
There are 14 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
742/53 = 14
Problem 5
742 apples need to be arranged in 7 baskets. How many apples will go on each basket?
Each basket will have 106 apples.
Explanation
Divide total apples with baskets.
742/7 = 106
FAQs on Factors of 742
1.What are the factors of 742?
2.Mention the prime factors of 742.
3.Is 742 a multiple of 53?
4.Mention the factor pairs of 742?
5.What is the square of 742?
6.How can children in Saudi Arabia use numbers in everyday life to understand Factors of 742?
7.What are some fun ways kids in Saudi Arabia can practice Factors of 742 with numbers?
8.What role do numbers and Factors of 742 play in helping children in Saudi Arabia develop problem-solving skills?
9.How can families in Saudi Arabia create number-rich environments to improve Factors of 742 skills?
Important Glossaries for Factor of 742
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 742 are 1, 2, 7, 53, 106, 371, and 742.
- Prime factors: The factors which are prime numbers. For example, 2, 7, and 53 are prime factors of 742.
- 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 742 are (1, 742), (2, 371), etc.
- Prime factorization: Expressing a number as the product of prime factors. For example, the prime factorization of 742 is 2 × 7 × 53.
- Multiple: A multiple of a number is the product of that number and an integer. For example, 742 is a multiple of 53.
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About BrightChamps in Saudi Arabia
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.
