120 LearnersLast updated on May 26th, 2025
Factors of 1649
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 1649, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1649?
The numbers that divide 1649 evenly are known as factors of 1649. A factor of 1649 is a number that divides the number without remainder. The factors of 1649 are 1, 17, 97, and 1649. Negative factors of 1649: -1, -17, -97, and -1649. Prime factors of 1649: 17 and 97. Prime factorization of 1649: 17 × 97. The sum of factors of 1649: 1 + 17 + 97 + 1649 = 1764
How to Find Factors of 1649?
Factors can be found using different methods. Mentioned below are some commonly used methods: Finding factors using multiplication Finding factors using the 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 1649. Identifying the numbers which are multiplied to get the number 1649 is the multiplication method. Step 1: Multiply 1649 by 1, 1649 × 1 = 1649. Step 2: Check for other numbers that give 1649 after multiplying 17 × 97 = 1649 Therefore, the positive factor pairs of 1649 are: (1, 1649) and (17, 97). All these factor pairs result in 1649. 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 1649 by 1, 1649 ÷ 1 = 1649. Step 2: Continue dividing 1649 by the numbers until the remainder becomes 0. 1649 ÷ 1 = 1649 1649 ÷ 17 = 97 Therefore, the factors of 1649 are: 1, 17, 97, 1649.
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 1649 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1. 1649 ÷ 17 = 97 97 ÷ 97 = 1 The prime factors of 1649 are 17 and 97. The prime factorization of 1649 is: 17 × 97.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows - Step 1: Firstly, 1649 is divided by 17 to get 97. Step 2: Here, 97 is a prime number, that cannot be divided anymore. So, the prime factorization of 1649 is: 17 × 97. 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 1649: (1, 1649) and (17, 97). Negative factor pairs of 1649: (-1, -1649) and (-17, -97).
Common Mistakes and How to Avoid Them in Factors of 1649
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 the factors for every word. Always remember to include 1 and the number itself. For example, in factors of 1649, 1 and 1649 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors. For example, the factors of 1649 consist of -1, -17, -97, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor. For example, thinking 1.5 as a factor, because 1649/1.5 = 1099.333, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes. For example, thinking all the factors of 1649 are prime numbers. For example, 17 and 97 are the prime factors of 1649, but it has other factors like 1, 1649.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors. For example, not breaking 1649 as 17 × 97 and missing all the key factors.
Factors of 1649 Examples
Problem 1
There are 17 workers and 1649 bricks. How will they distribute it equally?
They will get 97 bricks each.
Explanation
To divide the bricks equally, we need to divide the total bricks by the number of workers. 1649/17 = 97
Problem 2
A rectangular garden has a length of 97 meters and a total area of 1649 square meters. Find the width.
17 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width 1649 = 97 × width To find the value of width, we need to shift 97 to the left side. 1649/97 = width Width = 17.
Problem 3
There are 97 books and 1649 pages. How many pages will be in each book?
Each book will have 17 pages.
Explanation
To find the pages in each book, divide the total pages by the number of books. 1649/97 = 17
Problem 4
In a hall, there are 1649 seats, and 17 sections. How many seats are there in each section?
There are 97 seats in each section.
Explanation
Dividing the seats by the total sections, we will get the number of seats in each section. 1649/17 = 97
Problem 5
1649 apples need to be packed in 97 boxes. How many apples will go in each box?
Each of the boxes has 17 apples.
Explanation
Divide total apples by boxes. 1649/97 = 17
FAQs on Factors of 1649
1.What are the factors of 1649?
2.Mention the prime factors of 1649.
3.Is 1649 a multiple of 17?
4.Mention the factor pairs of 1649?
5.What is the square of 1649?
6.How can children in United States use numbers in everyday life to understand Factors of 1649?
7.What are some fun ways kids in United States can practice Factors of 1649 with numbers?
8.What role do numbers and Factors of 1649 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 1649 skills?
Important Glossaries for Factor of 1649
Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1649 are 1, 17, 97, and 1649. Prime factors: The factors which are prime numbers. For example, 17 and 97 are prime factors of 1649. 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 1649 are (1, 1649) and (17, 97). Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 1649 is 17 × 97. Multiple: A number that can be divided by another number without a remainder. For example, 1649 is a multiple of 1 and 17.
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About BrightChamps in United States
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.
