GCF of 25 and 35
2026-02-21 20:32 Diff
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Last updated on August 5, 2025

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 25 and 35.

What is the GCF of 25 and 35?

The greatest common factor of 25 and 35 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 25 and 35?

To find the GCF of 25 and 35, a few methods are described below:

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

GCF of 25 and 35 by Using Listing of factors

Steps to find the GCF of 25 and 35 using the listing of factors:

Step 1: Firstly, list the factors of each number:

Factors of 25 = 1, 5, 25.

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

Step 2: Now, identify the common factors of them Common factors of 25 and 35: 1, 5.

Step 3: Choose the largest factor.

The largest factor that both numbers have is 5.

The GCF of 25 and 35 is 5.

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GCF of 25 and 35 Using Prime Factorization

To find the GCF of 25 and 35 using the Prime Factorization Method, follow these steps:

Step 1: Find the prime factors of each number:

Prime Factors of 25: 25 = 5 x 5 = 5²

Prime Factors of 35: 35 = 5 x 7

Step 2: Now, identify the common prime factors.

The common prime factor is: 5

Step 3: Multiply the common prime factor.

The Greatest Common Factor of 25 and 35 is 5.

GCF of 25 and 35 Using Division Method or Euclidean Algorithm Method

Find the GCF of 25 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 25 35 ÷ 25 = 1 (quotient), The remainder is calculated as 35 − (25×1) = 10

The remainder is 10, not zero, so continue the process

Step 2: Now divide the previous divisor (25) by the previous remainder (10)

Divide 25 by 10

25 ÷ 10 = 2 (quotient), remainder = 25 − (10×2) = 5

Step 3: Divide 10 by the remainder (5) 10 ÷ 5 = 2 (quotient), remainder = 10 − (5×2) = 0

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

The GCF of 25 and 35 is 5.

Common Mistakes and How to Avoid Them in GCF of 25 and 35

Finding GCF of 25 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 baker has 25 chocolate muffins and 35 vanilla muffins. She wants to pack them into boxes, with the largest number of muffins in each box. How many muffins will be in each box?

Okay, lets begin

We should find the GCF of 25 and 35 GCF of 25 and 35 is 5.

There are 5 muffins in each box.

25 ÷ 5 = 5

35 ÷ 5 = 7

There will be 5 boxes, each containing 5 chocolate muffins and 7 vanilla muffins.

Explanation

As the GCF of 25 and 35 is 5, the baker can make 5 boxes.

Now divide 25 and 35 by 5.

Each box contains 5 chocolate muffins and 7 vanilla muffins.

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Problem 2

A gardener has 25 rose plants and 35 tulip plants. They want to plant them in rows with the same number of plants in each row, using the largest possible number of plants per row. How many plants will be in each row?

Okay, lets begin

GCF of 25 and 35 is 5. So each row will have 5 plants.

Explanation

There are 25 rose and 35 tulip plants.

To find the total number of plants in each row, we should find the GCF of 25 and 35.

There will be 5 plants in each row.

Well explained 👍

Problem 3

A tailor has 25 meters of silk fabric 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 25 and 35

The GCF of 25 and 35 is 5.

The fabric is 5 meters long.

Explanation

For calculating the longest length of the fabric, first, we need to calculate the GCF of 25 and 35, which is 5.

The length of each piece of fabric will be 5 meters.

Well explained 👍

Problem 4

A carpenter has two wooden planks, one 25 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?

Okay, lets begin

The carpenter needs the longest piece of wood

GCF of 25 and 35 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, 25 cm and 35 cm, respectively, we have to find the GCF of 25 and 35, which is 5 cm.

The longest length of each piece is 5 cm.

Well explained 👍

Problem 5

If the GCF of 25 and ‘b’ is 5, and the LCM is 175, find ‘b’.

Okay, lets begin

The value of ‘b’ is 35.

Explanation

GCF x LCM = product of the numbers

5 × 175 = 25 × b

875 = 25b

b = 875 ÷ 25 = 35

Well explained 👍

FAQs on the Greatest Common Factor of 25 and 35

1.What is the LCM of 25 and 35?

The LCM of 25 and 35 is 175.

2.Is 25 divisible by 5?

Yes, 25 is divisible by 5 because it is a multiple of 5.

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 prime numbers, it is said to be the GCF of any two prime numbers.

4.What is the prime factorization of 35?

The prime factorization of 35 is 5 x 7.

5.Are 25 and 35 prime numbers?

No, 25 and 35 are not prime numbers because both of them have more than two factors.

Important Glossaries for GCF of 25 and 35

  • Factors: Factors are numbers that divide the target number completely. For example, the factors of 25 are 1, 5, and 25.
  • Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 5 are 5, 10, 15, 20, 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 35 are 5 and 7.
  • Remainder: The value left after division when the number cannot be divided evenly. For example, when 35 is divided by 6, the remainder is 5 and the quotient is 5.
  • LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 25 and 35 is 175.

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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.