107 LearnersLast updated on May 26th, 2025
Factors of 629
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 629, how they are used in real life, and tips to learn them quickly.
What are the Factors of 629?
The numbers that divide 629 evenly are known as factors of 629. A factor of 629 is a number that divides the number without remainder. The factors of 629 are 1, 17, 37, and 629.
Negative factors of 629: -1, -17, -37, and -629.
Prime factors of 629: 17 and 37.
Prime factorization of 629: 17 × 37.
The sum of factors of 629: 1 + 17 + 37 + 629 = 684
How to Find Factors of 629?
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 629. Identifying the numbers which are multiplied to get the number 629 is the multiplication method.
Step 1: Multiply 629 by 1, 629 × 1 = 629.
Step 2: Check for other numbers that give 629 after multiplying 17 × 37 = 629
Therefore, the positive factor pairs of 629 are: (1, 629) and (17, 37). 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 in whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 629 by 1, 629 ÷ 1 = 629.
Step 2: Continue dividing 629 by the numbers until the remainder becomes 0.
629 ÷ 1 = 629
629 ÷ 17 = 37
629 ÷ 37 = 17
Therefore, the factors of 629 are: 1, 17, 37, 629.
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 629 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
629 ÷ 17 = 37
37 ÷ 37 = 1
The prime factors of 629 are 17 and 37. The prime factorization of 629 is: 17 × 37.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 629 is divided by 17 to get 37.
Step 2: 37 is already a prime number and cannot be divided further. So, the prime factorization of 629 is: 17 × 37.
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 629: (1, 629) and (17, 37).
- Negative factor pairs of 629: (-1, -629) and (-17, -37).
Common Mistakes and How to Avoid Them in Factors of 629
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 number. Always remember to include 1 and the number itself. For example, in factors of 629, 1 and 629 are also factors.
Factors of 629 Examples
Problem 1
A library has 629 books, and there are 17 shelves. How many books will be placed on each shelf?
Each shelf will have 37 books.
Explanation
To divide the books equally, we need to divide the total books by the number of shelves.
629/17 = 37
Problem 2
A classroom has 629 chairs arranged in 37 rows. How many chairs are there in each row?
There are 17 chairs in each row.
Explanation
To find the number of chairs in each row, divide the total chairs by the number of rows.
629/37 = 17
Problem 3
A farmer has 629 apples and wants to put them in baskets of 37. How many full baskets can he make?
He can make 17 full baskets.
Explanation
To find the full baskets, divide the total apples by the number of apples per basket.
629/37 = 17
Problem 4
629 students are to be divided into 17 teams. How many students will be in each team?
There will be 37 students in each team.
Explanation
Dividing the students by the total teams, we will get the number of students in each team.
629/17 = 37
Problem 5
A pizza restaurant has 629 slices of pizza, and they need to serve them in 1-slice servings. How many servings can they provide?
They can provide 629 servings.
Explanation
Divide the total number of pizza slices by the number of slices per serving.
629/1 = 629
FAQs on Factors of 629
1.What are the factors of 629?
2.Mention the prime factors of 629.
3.Is 629 a multiple of 17?
4.Mention the factor pairs of 629?
5.What is the square of 629?
Important Glossaries for Factors of 629
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 629 are 1, 17, 37, and 629.
- Prime factors: The factors that are prime numbers. For example, 17 and 37 are prime factors of 629.
- 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 629 are (1, 629) and (17, 37).
- Prime factorization: Expressing a number as the product of its prime factors. For example, the prime factorization of 629 is 17 × 37.
- Negative factors: Factors that are negative numbers. For example, -1, -17, -37, and -629 are negative factors of 629.
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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.
