GCF of 100 and 36
2026-02-21 20:35 Diff
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Last updated on September 9, 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 to schedule events. In this topic, we will learn about the GCF of 100 and 36.

What is the GCF of 100 and 36?

The greatest common factor of 100 and 36 is 4. 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 100 and 36?

To find the GCF of 100 and 36, a few methods are described below:

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

GCF of 100 and 36 by Using Listing of Factors

Steps to find the GCF of 100 and 36 using the listing of factors:

Step 1: Firstly, list the factors of each number Factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100. Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36.

Step 2: Now, identify the common factors of them Common factors of 100 and 36: 1, 2, 4.

Step 3: Choose the largest factor The largest factor that both numbers have is 4. The GCF of 100 and 36 is 4.

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GCF of 100 and 36 Using Prime Factorization

To find the GCF of 100 and 36 using the Prime Factorization Method, follow these steps:

Step 1: Find the prime factors of each number Prime Factors of 100: 100 = 2 x 2 x 5 x 5 = 2² x 5² Prime Factors of 36: 36 = 2 x 2 x 3 x 3 = 2² x 3²

Step 2: Now, identify the common prime factors The common prime factors are: 2 x 2 = 2²

Step 3: Multiply the common prime factors 2² = 4. The Greatest Common Factor of 100 and 36 is 4.

GCF of 100 and 36 Using Division Method or Euclidean Algorithm Method

Find the GCF of 100 and 36 using the division method or Euclidean Algorithm Method. Follow these steps:

Step 1: First, divide the larger number by the smaller number Here, divide 100 by 36 100 ÷ 36 = 2 (quotient), The remainder is calculated as 100 − (36×2) = 28. The remainder is 28, not zero, so continue the process.

Step 2: Now divide the previous divisor (36) by the previous remainder (28) Divide 36 by 28 36 ÷ 28 = 1 (quotient), remainder = 36 − (28×1) = 8. Continue the process: Divide 28 by 8 28 ÷ 8 = 3 (quotient), remainder = 28 − (8×3) = 4. Divide 8 by 4 8 ÷ 4 = 2 (quotient), remainder = 8 − (4×2) = 0.

The remainder is zero, the divisor will become the GCF. The GCF of 100 and 36 is 4.

Common Mistakes and How to Avoid Them in GCF of 100 and 36

Finding the GCF of 100 and 36 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 gardener has 100 tulips and 36 roses. 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?

Okay, lets begin

We should find the GCF of 100 and 36. GCF of 100 and 36 2² = 4. There are 4 equal groups. 100 ÷ 4 = 25 36 ÷ 4 = 9 There will be 4 groups, and each group gets 25 tulips and 9 roses.

Explanation

As the GCF of 100 and 36 is 4, the gardener can make 4 groups.

Now divide 100 and 36 by 4.

Each group gets 25 tulips and 9 roses.

Well explained 👍

Problem 2

A concert hall has 100 blue seats and 36 red seats. They want to arrange them in rows with the same number of seats in each row, using the largest possible number of seats per row. How many seats will be in each row?

Okay, lets begin

GCF of 100 and 36 2² = 4. So each row will have 4 seats.

Explanation

There are 100 blue and 36 red seats.

To find the total number of seats in each row, we should find the GCF of 100 and 36.

There will be 4 seats in each row.

Well explained 👍

Problem 3

A tailor has 100 meters of silk ribbon and 36 meters of cotton 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?

Okay, lets begin

For calculating the longest equal length, we have to calculate the GCF of 100 and 36. The GCF of 100 and 36 2² = 4. The ribbon is 4 meters long.

Explanation

For calculating the longest length of the ribbon, first, we need to calculate the GCF of 100 and 36, which is 4.

The length of each piece of the ribbon will be 4 meters.

Well explained 👍

Problem 4

A carpenter has two wooden planks, one 100 cm long and the other 36 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 100 and 36 2² = 4. The longest length of each piece is 4 cm.

Explanation

To find the longest length of each piece of the two wooden planks, 100 cm and 36 cm, respectively, we have to find the GCF of 100 and 36, which is 4 cm.

The longest length of each piece is 4 cm.

Well explained 👍

Problem 5

If the GCF of 100 and ‘b’ is 4, and the LCM is 900. Find ‘b’.

Okay, lets begin

The value of ‘b’ is 36.

Explanation

GCF x LCM = product of the numbers

4 x 900

= 100 x b 3600

= 100b b

= 3600 ÷ 100 = 36

Well explained 👍

FAQs on the Greatest Common Factor of 100 and 36

1.What is the LCM of 100 and 36?

The LCM of 100 and 36 is 900.

2.Is 100 divisible by 5?

Yes, 100 is divisible by 5 because it ends in a 0.

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 36?

The prime factorization of 36 is 2² x 3².

5.Are 100 and 36 prime numbers?

No, 100 and 36 are not prime numbers because both of them have more than two factors.

Important Glossaries for GCF of 100 and 36

  • Factors: Factors are numbers that divide the target number completely. For example, the factors of 8 are 1, 2, 4, and 8.
  • Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 3 are 3, 6, 9, 12, 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 20 are 2 and 5.
  • Remainder: The value left after division when the number cannot be divided evenly. For example, when 14 is divided by 5, the remainder is 4, 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.

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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.