262 LearnersLast updated on May 26th, 2025
Factors of 77
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 77 easily.
What are the Factors of 77?
Factors of 77 are those numbers that can divide 77 perfectly. The factors of 77 are:
1,7,11 and 77.
Negative factors of 77: -1, -7, -11, -77.
Prime factors of 77: 7,11
Prime factorization of 77: 7×11
The sum of factors of 77: 1+7+11+77 = 96
How to Find the Factors of 77
For finding factors of 77, 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 77. Let us find the pairs which, on multiplication, yields 77.
1×77=77
7×11=77
From this, we conclude that, factors of 77 are: 1,7,11, and 77.
Finding Factors using Division Method
The division method finds the numbers that evenly divides the given number 77. To find the factors of 77, we have to divide 77 by all possible natural numbers less than 77 and check.
1,7,11,77 are the only factors that the number 77 has. So to verify the factors of 77 using the division method, we just need to divide 77 by each factor.
77/1 =77
77/7 =11
77/11=7
77/77=1
Prime Factors and Prime Factorization
Prime Factorization is the easiest process to find prime factors. It decomposes 77 into a product of its prime integers.
Prime Factors of 77: 7,11.
Prime Factorization of 77: 7×11
Factor tree
The number 77 is written on top and two branches are extended.
Fill in those branches with a factor pair of the number above, i.e., 77.
Continue this process until each branch ends with a prime factor (number).
The first two branches of the factor tree of 77 are 7 and 11.
Factor Pairs
Positive pair factors: (1,77), (7,11)
Negative pair factors: (-1,-77), (-7,-77).
Common Mistakes and How to Avoid Them in Factors of 77
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 77 Examples
Problem 1
A lady has 77 dahlias and 154 roses. She wants to divide them equally among some vases. What is the maximum number of vases she requires?
Number of dahlias: 77
Number of roses: 154
Factors of 77: 1,7,11,77
Factors of 154: 1,2,7,11,14,22,77,154
Common factors of 77 and 154: 1,7,11,77.
Greatest common factor of 77 and 154: 77
So, there will be 77 vases she requires.
Answer: 77 vases
Explanation
To divide equally, the maximum number of plates can be found through the Greatest Common Factor. Here, we found the GCF, which is the answer.
Problem 2
Find the simplest form of square root of 77.
√77 = √(7×11) = √77
Answer: The simplest form of square root of 77 is √77.
Explanation
Break down 77 into its product of its prime factor and find its square root by grouping a pair of factors at a time, leaving the remaining single factors under radical.
Problem 3
The area of a rectangle is 77 square units. If the length is 11 units, then what is the measure of its width?
Area of rectangle: 77 sq units
Factors of 77: 1,7,11,77
We know that the area of a rectangle is the product of its length and breadth.
Given, length= 11 units
There exists a factor pair of 77, which is (7,11). Hence, width is 7 units. Let’s check it through the formula for area.
So, length×width = area
⇒ 11 × width = 77
⇒ width = 77/11 = 7
Answer: 7 units
Explanation
Used the concept of factor pairs for 77 and rechecked using the formula for finding area of a rectangle.
Problem 4
Find the smallest number that is divisible by 7 and 77.
Prime factorization of 7: 7×1.
Prime factorization of 77: 7×11
LCM of 7 and 77: 7×11 = 77
Answer: 77 is the smallest number which is divisible by 7 and 77.
Explanation
To find the smallest number which is divisible by 7 and 77, we need to find the LCM of these numbers.
Problem 5
If a number is divisible by both 7 and 11, is it divisible by 77?
Yes, any number which is divisible by 7 and 11 is also divisible by 77, since 77 = 7×11
Answer: Yes
Explanation
Any number which is divisible by the factor 7 and factor 11 of 77, then it is also divisible by 77 because 77 is a product of 7 and 11.
FAQs on Factors of 77
1.Is 77 a prime number?
2.What is 77 divisible by?
3. Is 77 a perfect square?
4.Is 7 a factor of 777?
5.Is 7 a factor of 1000?
6.How can children in India use numbers in everyday life to understand Factors of 77?
7.What are some fun ways kids in India can practice Factors of 77 with numbers?
8.What role do numbers and Factors of 77 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of 77 skills?
Important Glossaries for Factors of 77
- 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.
