101 LearnersLast updated on August 5th, 2025
GCF of 70 and 95
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, group or arrange items, and schedule events. In this topic, we will learn about the GCF of 70 and 95.
What is the GCF of 70 and 95?
The greatest common factor of 70 and 95 is 5. The largest divisor of two or more numbers is called the GCF of the numbers. If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1. The GCF of two numbers cannot be negative because divisors are always positive.
How to find the GCF of 70 and 95?
To find the GCF of 70 and 95, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / Euclidean Algorithm
GCF of 70 and 95 by Using Listing of factors
Steps to find the GCF of 70 and 95 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70.
Factors of 95 = 1, 5, 19, 95.
Step 2: Now, identify the common factors of them Common factors of 70 and 95: 1, 5.
Step 3: Choose the largest factor
The largest factor that both numbers have is 5.
The GCF of 70 and 95 is 5.
GCF of 70 and 95 Using Prime Factorization
To find the GCF of 70 and 95 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 70: 70 = 2 x 5 x 7
Prime Factors of 95: 95 = 5 x 19
Step 2: Now, identify the common prime factors
The common prime factors are: 5
Step 3: Multiply the common prime factors 5 = 5.
The Greatest Common Factor of 70 and 95 is 5.
GCF of 70 and 95 Using Division Method or Euclidean Algorithm Method
Find the GCF of 70 and 95 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 95 by 70 95 ÷ 70 = 1 (quotient),
The remainder is calculated as 95 − (70×1) = 25
The remainder is 25, not zero, so continue the process
Step 2: Now divide the previous divisor (70) by the previous remainder (25)
Divide 70 by 25 70 ÷ 25 = 2 (quotient), remainder = 70 − (25×2) = 20
Step 3: Continue with 25 divided by 20 25 ÷ 20 = 1 (quotient), remainder = 25 − (20×1) = 5
Step 4: Now divide 20 by 5 20 ÷ 5 = 4 (quotient), remainder = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 70 and 95 is 5.
Common Mistakes and How to Avoid Them in GCF of 70 and 95
Finding the GCF of 70 and 95 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
Mistake 1
Listing Incorrect Factors
Students may sometimes list incorrect factors.
For example, while listing factors of 70, students may mention 8, which is incorrect. To avoid this, students should carefully divide the number and list the factors correctly.
Mistake 2
Choosing the wrong common factor
Students may sometimes select the smallest common factor instead of the largest one. To avoid this confusion, students should list all the common factors and find the greatest one.
Mistake 3
Forgetting to include 1 as a factor
Sometimes students may forget 1 as a common factor of the numbers. However, it does not affect the GCF, but it tells about the incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples instead of factors
Students confuse between factors and multiples. In that confusion, sometimes they may write multiples instead of factors. To avoid this confusion, students should know the definitions of multiples and factors clearly.
Mistake 5
Assuming GCF is always an even number
Students may assume that the GCF of two numbers will always be an even number. But it's not true that a GCF can also be an odd number. To avoid this, students should focus on common factors rather than focusing on even and odd numbers.
Greatest Common Factor of 70 and 95 Examples
Problem 1
A teacher has 70 pencils and 95 erasers. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?
We should find the GCF of 70 and 95 GCF of 70 and 95 is 5.
There are 5 equal groups 70 ÷ 5 = 14
95 ÷ 5 = 19
There will be 5 groups, and each group gets 14 pencils and 19 erasers.
Explanation
As the GCF of 70 and 95 is 5, the teacher can make 5 groups. Now divide 70 and 95 by 5. Each group gets 14 pencils and 19 erasers.
Problem 2
A school has 70 red chairs and 95 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?
GCF of 70 and 95 is 5.
So, each row will have 5 chairs.
Explanation
There are 70 red and 95 blue chairs. To find the total number of chairs in each row, we should find the GCF of 70 and 95. There will be 5 chairs in each row.
Problem 3
A tailor has 70 meters of red ribbon and 95 meters of blue ribbon. She wants to cut both ribbons into pieces of equal length, using the longest possible length. What should be the length of each piece?
For calculating the longest equal length, we have to calculate the GCF of 70 and 95.
The GCF of 70 and 95 is 5.
The ribbon is 5 meters long.
Explanation
For calculating the longest length of the ribbon, first, we need to calculate the GCF of 70 and 95, which is 5. The length of each piece of the ribbon will be 5 meters.
Problem 4
A carpenter has two wooden planks, one 70 cm long and the other 95 cm long. He wants to cut them into the longest possible equal pieces, without any wood left over. What should be the length of each piece?
The carpenter needs the longest piece of wood GCF of 70 and 95 is 5.
The longest length of each piece is 5 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 70 cm and 95 cm, respectively, we have to find the GCF of 70 and 95, which is 5 cm. The longest length of each piece is 5 cm.
Problem 5
If the GCF of 70 and ‘a’ is 5, and the LCM is 665. Find ‘a’.
The value of ‘a’ is 95.
Explanation
GCF x LCM = product of the numbers 5 × 665 = 70 × a
3325 = 70a
a = 3325 ÷ 70 = 47.5
Correct calculation should have been: GCF x LCM = product of the numbers 5 × 665 = 70 × a
3325 = 70a
a = 3325 ÷ 70 = 47.5
The calculation was wrong, as 665 cannot be the LCM with such GCF and a value.
Correcting it: 5 × 1330 = 70 × a 6650 = 70a a = 6650 ÷ 70 = 95
FAQs on the Greatest Common Factor of 70 and 95
1.What is the LCM of 70 and 95?
2.Is 70 divisible by 5?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 95?
5.Are 70 and 95 prime numbers?
6.How can children in United States use numbers in everyday life to understand GCF of 70 and 95?
7.What are some fun ways kids in United States can practice GCF of 70 and 95 with numbers?
8.What role do numbers and GCF of 70 and 95 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve GCF of 70 and 95 skills?
Important Glossaries for GCF of 70 and 95
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 10 are 1, 2, 5, and 10.
- Prime Factors: These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factors of 20 are 2 and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 13 is divided by 5, the remainder is 3 and the quotient is 2.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 8 and 12 is 24.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 70 and 95 is 5, as it is their largest common factor that divides the numbers completely.
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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.
