GCF of 7 and 35
2026-02-28 13:14 Diff
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Last updated on September 19, 2025

The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, to group or arrange items, and to schedule events. In this topic, we will learn about the GCF of 7 and 35.

What is the GCF of 7 and 35?

The greatest common factor of 7 and 35 is 7. The largest divisor of two or more numbers is called the GCF of the number. 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 7 and 35?

To find the GCF of 7 and 35, a few methods are described below 

  • Listing Factors
     
  • Prime Factorization
     
  • Long Division Method / by Euclidean Algorithm

GCF of 7 and 35 by Using Listing of factors

Steps to find the GCF of 7 and 35 using the listing of factors

Step 1: Firstly, list the factors of each number

Factors of 7 = 1, 7.

Factors of 35 = 1, 5, 7, 35.

Step 2: Now, identify the common factors of them Common factors of 7 and 35: 1, 7.

Step 3: Choose the largest factor The largest factor that both numbers have is 7.

The GCF of 7 and 35 is 7.

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GCF of 7 and 35 Using Prime Factorization

To find the GCF of 7 and 35 using the Prime Factorization Method, follow these steps:

Step 1: Find the prime factors of each number

Prime Factors of 7: 7 = 7

Prime Factors of 35: 35 = 5 x 7

Step 2: Now, identify the common prime factors The common prime factor is: 7

Step 3: Multiply the common prime factors 7 = 7.

The Greatest Common Factor of 7 and 35 is 7.

GCF of 7 and 35 Using Division Method or Euclidean Algorithm Method

Find the GCF of 7 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 35 by 7 35 ÷ 7 = 5 (quotient),

The remainder is calculated as 35 − (7×5) = 0

The remainder is zero, so the divisor will become the GCF.

The GCF of 7 and 35 is 7.

Common Mistakes and How to Avoid Them in GCF of 7 and 35

Finding the GCF of 7 and 35 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.

Problem 1

A farmer has 7 apple trees and 35 orange trees. He wants to plant them in rows with the largest possible number of trees in each row. How many trees will be in each row?

Okay, lets begin

We should find the GCF of 7 and 35 GCF of 7 and 35 7.

So each row will have 7 trees.

Explanation

As the GCF of 7 and 35 is 7, the farmer can make rows of 7 trees.

Well explained 👍

Problem 2

A baker has 7 loaves of bread and 35 pastries. They want to pack them in boxes with an equal number of items, using the largest possible number of items per box. How many items will be in each box?

Okay, lets begin

GCF of 7 and 35 7.

So each box will have 7 items.

Explanation

There are 7 loaves of bread and 35 pastries.

To find the total number of items in each box, we should find the GCF of 7 and 35.

There will be 7 items in each box.

Well explained 👍

Problem 3

A seamstress has 7 meters of silk and 35 meters of cotton 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?

Okay, lets begin

For calculating the longest equal length, we have to calculate the GCF of 7 and 35

The GCF of 7 and 35 7.

The fabric pieces will be 7 meters long.

Explanation

For calculating the longest length of the fabric first, we need to calculate the GCF of 7 and 35, which is 7.

The length of each piece of fabric will be 7 meters.

Well explained 👍

Problem 4

A gardener has two lengths of hose, one 7 meters long and the other 35 meters long. He wants to cut them into the longest possible equal pieces without any hose left over. What should be the length of each piece?

Okay, lets begin

The gardener needs the longest piece of hose GCF of 7 and 35 7.

The longest length of each piece is 7 meters.

Explanation

To find the longest length of each piece of the two hoses, 7 meters and 35 meters, respectively, we have to find the GCF of 7 and 35, which is 7 meters.

The longest length of each piece is 7 meters.

Well explained 👍

Problem 5

If the GCF of 7 and ‘b’ is 7, and the LCM is 35, find ‘b’.

Okay, lets begin

The value of ‘b’ is 35.

Explanation

GCF x LCM = product of the numbers

7 × 35 = 7 × b

245 = 7b

b = 245 ÷ 7 = 35

Well explained 👍

FAQs on the Greatest Common Factor of 7 and 35

1.What is the LCM of 7 and 35?

The LCM of 7 and 35 is 35.

2.Is 7 a prime number?

Yes, 7 is a prime number because its only divisors are 1 and 7.

3.What will be the GCF of any two prime numbers?

The common factor of prime numbers is 1 and the number itself. Since 1 is the only common factor of any two different prime numbers, it is said to be the GCF of any two different prime numbers.

4.What is the prime factorization of 35?

The prime factorization of 35 is 5 x 7.

5.Are 7 and 35 prime numbers?

No, 7 is a prime number, but 35 is not because it has more than two factors.

Important Glossaries for GCF of 7 and 35

  • Factors: Factors are numbers that divide the target number completely. For example, the factors of 35 are 1, 5, 7, and 35.
  • Prime Number: A number that has only two factors, 1 and itself. For example, 7 is a prime number.
  • 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 35 are 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 and the quotient is 3.
  • GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 7 and 35 is 7, 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.