Last updated on May 26th, 2025
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.
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.
For finding factors of 78, we will be learning these below-mentioned 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.
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 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
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).
Children quite often make silly mistakes while solving factors. Let us see what are the common errors to occur and how to avoid them
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
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.
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
First find the LCM and just add the remainder with that to get the smallest number.
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
Used the concept of factor pairs for 78 and rechecked using the formula for finding area of a rectangle.
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.
To find the smallest number which is divisible by 2,6,26, we need to find the LCM of these numbers.
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
Added all the factors togather to get the sum.
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.
: She loves to read number jokes and games.