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101 LearnersLast updated on September 9, 2025
GCF of 70 and 35
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share the items equally, to group or arrange items and schedule events. In this topic, we will learn about the GCF of 70 and 35.
What is the GCF of 70 and 35?
The greatest common factor of 70 and 35 is 35. 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 35?
To find the GCF of 70 and 35, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 70 and 35 by Using Listing of factors
Steps to find the GCF of 70 and 35 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 35 = 1, 5, 7, 35.
Step 2: Now, identify the common factors of them Common factors of 70 and 35: 1, 5, 7, 35.
Step 3: Choose the largest factor The largest factor that both numbers have is 35. The GCF of 70 and 35 is 35.
GCF of 70 and 35 Using Prime Factorization
To find the GCF of 70 and 35 using Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 70: 70 = 2 × 5 × 7 Prime Factors of 35: 35 = 5 × 7
Step 2: Now, identify the common prime factors The common prime factors are: 5 × 7
Step 3: Multiply the common prime factors 5 × 7 = 35. The Greatest Common Factor of 70 and 35 is 35.
GCF of 70 and 35 Using Division Method or Euclidean Algorithm Method
Find the GCF of 70 and 35 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 70 by 35 70 ÷ 35 = 2 (quotient), The remainder is calculated as 70 − (35×2) = 0 The remainder is zero, so the divisor becomes the GCF. The GCF of 70 and 35 is 35.
Common Mistakes and How to Avoid Them in GCF of 70 and 35
Finding GCF of 70 and 35 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 20, 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 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 35 Examples
Problem 1
A gardener has 70 tulip bulbs and 35 daffodil bulbs. She wants to plant them in equal rows, with the largest number of bulbs in each row. How many bulbs will be in each row?
We should find GCF of 70 and 35 GCF of 70 and 35 5 × 7 = 35. There are 35 equal groups 70 ÷ 35 = 2 35 ÷ 35 = 1 There will be 35 bulbs in each row.
Explanation
As the GCF of 70 and 35 is 35, the gardener can make rows with 35 bulbs.
Divide 70 and 35 by 35, resulting in 2 rows of tulips and 1 row of daffodils per group.
Problem 2
A chef has 70 apples and 35 oranges. They want to place them in baskets with the same number of fruits in each basket, using the largest possible number of fruits per basket. How many fruits will be in each basket?
GCF of 70 and 35 5 × 7 = 35. So each basket will have 35 fruits.
Explanation
There are 70 apples and 35 oranges.
To find the total number of fruits in each basket, we should find the GCF of 70 and 35.
There will be 35 fruits in each basket.
Problem 3
A seamstress has 70 meters of cotton fabric and 35 meters of silk fabric. She wants to cut both fabrics into pieces of equal length, using the longest possible length. What should be the length of each piece?
For calculating longest equal length, we have to calculate the GCF of 70 and 35 The GCF of 70 and 35 5 × 7 = 35. The fabric pieces will be 35 meters long.
Explanation
To calculate the longest length of fabric pieces, we need to calculate the GCF of 70 and 35, which is 35.
The length of each piece of fabric will be 35 meters.
Problem 4
A carpenter has two wooden planks, one 70 cm long and the other 35 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 35 5 × 7 = 35. The longest length of each piece is 35 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 70 cm and 35 cm, respectively, we have to find the GCF of 70 and 35, which is 35 cm.
The longest length of each piece is 35 cm.
Problem 5
If the GCF of 70 and ‘b’ is 35, and the LCM is 140. Find ‘b’.
The value of ‘b’ is 140.
Explanation
GCF × LCM = product of the numbers
35 × 140
= 70 × b 4900
= 70b b
= 4900 ÷ 70 = 140
FAQs on the Greatest Common Factor of 70 and 35
1.What is the LCM of 70 and 35?
2.Is 70 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 35?
5.Are 70 and 35 prime numbers?
Important Glossaries for GCF of 70 and 35
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 35 are 1, 5, 7, and 35.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 7 are 7, 14, 21, 28, and so on.
- 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 70 are 2, 5, and 7.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 3, the remainder is 1.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 70 and 35 is 70.
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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.
