241 LearnersLast updated on May 26th, 2025
Factors of 129
Factors of any number are the dividers or multipliers that can divide the number fully and can be multiplied together to produce the given product, 129. Do you know, factors form the basic approach to solve some general mathematical procedures? This article will give you the insights of factors of 129.
What are the Factors of 129?
The factors of 129 or the numbers which divide 129 exactly are:
1,3,43, and 129.
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Negative factors of 129 |
-1,-3,-43,-129 |
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Prime factors of 129 |
3,43 |
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Prime factorization of 129 |
3×43 |
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The sum of factors of 129 |
1+3+43+129 = 176 |
How to Find the Factors of 129
For finding factors of 129, we will be learning these below-mentioned methods:
- Multiplication Method
- Division Method
- Prime Factor and Prime Factorization
- Factor Tree
Finding Factors using Multiplication Methods
This particular method often finds the pair of factors which, on multiplication together, produces 129. Let us find the pairs which, on multiplication, yields 129.
- 1×129=129
- 3×43=129
So, factors of 129 are: 1,3,43, and 129.
Finding Factors using Division Method
The division method finds the factors that evenly divides the given number 129. In this process, we have to divide 129 by all possible natural numbers less than 129 and check.
1,3,43, and 129 are the only factors that the number 129 has. So to verify the factors of 129 using the division method, we just need to divide 129 by each factor.
- 129/1 =129
- 129/3=43
- 129/43=3
- 129/129=1
Prime Factors and Prime Factorization
Prime Factorization is the easiest process to find prime factors. It decomposes 129 into a product of its prime integers.
- Prime Factors of 129: 3,43.
- Prime Factorization of 129: 3×43
Factor tree
The number 129 is written on top and two branches are extended.
Fill in those branches with a factor pair of the number above, i.e., 129.
Continue this process until each branch ends with a prime factor (number).
The first two branches of the factor tree of 129 are 3 and 43.
Factor Pairs
Positive pair factors: (1,129), (3,43).
Negative pair factors: (-1,-129), (-3,-43).
Common Mistakes and How to Avoid Them in Factors of 129
Solving problems based on factors can, sometimes, lead to misconceptions among children. Let us check what the common errors are and how to avoid them.
Mistake 1
Factors might be larger than the given number.
Factors can never be larger than the given number, but multiples can be. You need to understand the concept that factors are integers which divide a given number perfectly, and multiples are the products we get when the original number is multiplied with different numbers.
Factors of 129 Examples
Problem 1
Find the GCF of 129 and 130
Factors of 129: 1,3,43,129
Factors of 130: 1,2,5,10,13,26,65,130
Common factors of 129 and 130: 1
So, the Greatest Common Factor of 129 and 130 is 1.
Answer: 1
Explanation
We first listed out the factors of 129 and 130 and then found the common factors and then identified the greatest common factor from the common list.
Problem 2
Find the smallest number which, when divided by 3,43 and 129, leaves a remainder 2 in each case
First finding the LCM of 3,43,123
Prime factorization of 3 =3×1
Prime factorization of 43 = 43×1
Prime factorization of 129 = 3×43
LCM of 3,43,129 = 3×43=129
The smallest number which, when divided by 3,43 and 129, leaves a remainder 2 in each case is
= LCM + 2 = 129+2 =131
Answer: 131
Explanation
First find the LCM and just add the remainder with that to get the smallest number.
Problem 3
The area of a rectangle is 129 square units. If the length is 43 units, then what is the measure of its width?
Area of rectangle: 129 sq units
Factors of 129: 1,3,43,129
We know that the area of a rectangle is the product of its length and breadth.
Given, length= 43 units
There exists a factor pair of 129, which is (3,43). Hence, width is 3 units. Let’s check it through the formula for area.
So, length×width = area
⇒ 43 × width = 129
⇒ width = 129/43 = 3
Answer: 3 units
Explanation
Used the concept of factor pairs for 129 and rechecked using the formula for finding area of a rectangle.
Problem 4
Find the smallest number that is divisible by 3,43.
Prime factorization of 3: 3×1.
Prime factorization of 43: 43×1
LCM of 3,43: 3×43 = 129
Answer: 129 is the smallest number which is divisible by 3 and 43.
Explanation
To find the smallest number which is divisible by 3,43, we need to find the LCM of these numbers.
Problem 5
What is the sum of the factors of 129 and 128?
Factors of 129: 1,3,43,129
Sum of the factors: 1+3+43+129= 176
Factors of 128: 1,2,4,8,16,32,64,128
Explanation
Sum of the factors: 1+2+4+8+16+32+64+128 =255
FAQs on Factors of 129
1.What can you multiply to get 129?
2.What perfect square goes into 129?
3.What can 129 be divided by?
4.What is the factor tree of 129?
5. Is 129 a perfect cube?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of 129?
7.What are some fun ways kids in United Kingdom can practice Factors of 129 with numbers?
8.What role do numbers and Factors of 129 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Factors of 129 skills?
Important Glossaries for Factors of 129
- Multipliers - Number which multiplies or a number by which another number is multiplied.
- Dividers - A number that divides.
- Prime Factorization - It involves factoring the number into its prime factors.
- Prime factors - These are the prime numbers which on multiplication together results into the original number whose prime factors are to be obtained.
- Composite numbers - These are numbers having more than two factors.
- Multiple - It is a product of the given number and any other integer.
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About BrightChamps in United Kingdom
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.
