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162 LearnersLast updated on December 10th, 2024
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
Factors of 78 Examples
Problem 1
Find the GCF of 78 and 75
Explanation
Problem 2
Find the smallest number which, when divided by 26,39 and 78, leaves a remainder 3 in each case.
Explanation
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?
Explanation
Problem 4
Find the smallest number that is divisible by 2,6,26.
Explanation
Problem 5
What is the sum of the factors of 78 and 79?
Explanation
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?
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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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.
