248 LearnersLast updated on May 26th, 2025
Factors of 78
Factors of any number are the whole numbers that can divide the number completely. Why are factors important to learn? For mathematical approaches, factors are used in organizing and bringing more efficiency to any task. In this article, let's learn how to solve factors of 78 easily.
What are the Factors of 78?
Factors of 78 are those numbers that can divide 78 perfectly. The factors of 78 are:
1,2,3,6,13,26,39, and 78.
- Negative factors of 78: -1, -2, -3 -6, -13, -26, -39, -78
- Prime factors of 78: 2,3
- Prime factorization of 78: 3×2×13
- The sum of factors of 78: 1+2+3+6+13+26+39+78= 168
How to Find the Factors of 78
For finding factors of 78, 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 78. Let us find the pairs which, on multiplication, yields 78.
1×78=78
2×39=78
3×26=78
6×13=78
From this, we conclude that, factors of 78 are:1,2,3,6,13,26,39, and 78.
Finding Factors using Division Method
The division method finds the numbers that evenly divides the given number 78. To find the factors of 78, we have to divide 78 by all possible natural numbers less than 78 and check.
1,2,3,6,13,26,39,78 are the only factors that the number 78 has. So to verify the factors of 78 using the division method, we just need to divide 78 by each factor.
78/1 =78
78/2 =39
78/3=26
78/6=13
78/13=6
78/26=3
78/39=2
78/78=1
Prime Factors and Prime Factorization
Prime Factorization is the easiest process to find prime factors. It decomposes 78 into a product of its prime integers.
Prime Factors of 78: 2,3.
Prime Factorization of 78: 3×2×13
Factor tree
The number 78 is written on top and two branches are extended.
Fill in those branches with a factor pair of the number above, i.e., 78.
Continue this process until each branch ends with a prime factor (number).
The first two branches of the factor tree of 78 are 2 and 39, then proceeding to 39, we get 3 and 13.
Factor Pairs
Positive pair factors: (1,78), (2,39), (3,26), (6,13)
Negative pair factors: (-1,-78), (-2,-39), (-3,-26), (-6,-13).
Common Mistakes and How to Avoid Them in Factors of 78
Children quite often make silly mistakes while solving factors. Let us see what are the common errors to occur and how to avoid them
Mistake 1
Misconception and confusion about factors with that of multiples.
Factors are way different from multiples. You need to understand it clearly that factors are integers which divide a given number evenly, and multiples are the products we get when the original number is multiplied with different numbers.
Factors of 78 Examples
Problem 1
Find the GCF of 78 and 75
Factors of 78: 1,2,3,6,13,26,39,78
Factors of 75: 1,3,5,15,25,75
Common factors of 78 and 75: 1,3
So, the Greatest Common Factor of 78 and 75 is 3.
Answer: 3
Explanation
We first listed out the factors of 75 and 78 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 26,39 and 78, leaves a remainder 3 in each case.
First finding the LCM of 26,39,78
Prime factorization of 26 =13×2
Prime factorization of 39 = 13×3
Prime factorization of 78 = 3×2×13
LCM of 26,39,78 = 13×2×3=78
The smallest number which, when divided by 26,39 and 78, leaves a remainder 3 in each case is = LCM + 3 = 78+3 =81
Answer: 81
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 78 square units. If the length is 13 units, then what is the measure of its width?
Area of rectangle: 78 sq units
Factors of 78: 1,2,3,6,13,26,39,78
We know that the area of a rectangle is the product of its length and breadth.
Given, length= 13 units
There exists a factor pair of 78, which is (6,13). Hence, width is 6 units. Let’s check it through the formula for area.
So, length×width = area
⇒ 13 × width = 78
⇒ width = 78/13 = 6
Answer: 6 units
Explanation
Used the concept of factor pairs for 78 and rechecked using the formula for finding area of a rectangle.
Problem 4
Find the smallest number that is divisible by 2,6,26.
Prime factorization of 2: 2×1.
Prime factorization of 6: 3×2
Prime factorization of 26: 13×2
LCM of 2,6,26: 2×3×13 = 78
Answer: 78 is the smallest number which is divisible by 2,6, and 26.
Explanation
To find the smallest number which is divisible by 2,6,26, we need to find the LCM of these numbers.
Problem 5
What is the sum of the factors of 78 and 79?
Factors of 78: 1,2,3,6,13,26,39,78
Sum of the factors: 1+2+3+6+13+26+39+78= 168
Factors of 79: 1,79
Sum of the factors: 1+79 =80
Explanation
Added all the factors togather to get the sum.
FAQs on Factors of 78
1.What are the multiples of 78?
2.What times table equals 78?
3.Is 78 divisible by 7?
4.What are all 79 factors?
5.What is the LCM of 78 and 104?
6.How can children in Canada use numbers in everyday life to understand Factors of 78?
7.What are some fun ways kids in Canada can practice Factors of 78 with numbers?
8.What role do numbers and Factors of 78 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 78 skills?
Important Glossaries for Factors of 78
- Ratio - Ratio of two numbers compares between them, how many times one number contains the other number. It is expressed as m:n, where m and n are two positive numbers whose ratio is to be shown.
- Factors - These are numbers that divide the given number without leaving any remainder or the remainder as 0.
- 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 Canada
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.
