A day full of math games & activities. Find one near you.

GCF of 12 and 100

GCF of 12 and 100 is the largest possible number that divides 12 and 100 exactly without any remainder. The factors of 12 and 100 are 1, 2, 3, 4, 6, 12 and 1, 2, 4, 5, 10, 20, 25, 50, 100 respectively. There are 3 commonly used methods to find the GCF of 12 and 100 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 12 and 100
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 12 and 100?

Answer: GCF of 12 and 100 is 4.

Explanation:

The GCF of two non-zero integers, x(12) and y(100), is the greatest positive integer m(4) that divides both x(12) and y(100) without any remainder.

Methods to Find GCF of 12 and 100

The methods to find the GCF of 12 and 100 are explained below.

Prime Factorization Method
Listing Common Factors
Long Division Method

GCF of 12 and 100 by Prime Factorization

Prime factorization of 12 and 100 is (2 × 2 × 3) and (2 × 2 × 5 × 5) respectively. As visible, 12 and 100 have common prime factors. Hence, the GCF of 12 and 100 is 2 × 2 = 4.

GCF of 12 and 100 by Listing Common Factors

Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100

There are 3 common factors of 12 and 100, that are 1, 2, and 4. Therefore, the greatest common factor of 12 and 100 is 4.

GCF of 12 and 100 by Long Division

GCF of 12 and 100 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 100 (larger number) by 12 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (12) by the remainder (4).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the GCF of 12 and 100.

☛ Also Check:

GCF of 12 and 100 Examples

Example 1: Find the greatest number that divides 12 and 100 exactly.

Solution:

The greatest number that divides 12 and 100 exactly is their greatest common factor, i.e. GCF of 12 and 100.
⇒ Factors of 12 and 100:
- Factors of 12 = 1, 2, 3, 4, 6, 12
- Factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100
Therefore, the GCF of 12 and 100 is 4.
Example 2: The product of two numbers is 1200. If their GCF is 4, what is their LCM?

Solution:

Given: GCF = 4 and product of numbers = 1200
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1200/4
Therefore, the LCM is 300.
Example 3: For two numbers, GCF = 4 and LCM = 300. If one number is 100, find the other number.

Solution:

Given: GCF (x, 100) = 4 and LCM (x, 100) = 300
∵ GCF × LCM = 100 × (x)
⇒ x = (GCF × LCM)/100
⇒ x = (4 × 300)/100
⇒ x = 12
Therefore, the other number is 12.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on GCF of 12 and 100

What is the GCF of 12 and 100?

The GCF of 12 and 100 is 4. To calculate the GCF (Greatest Common Factor) of 12 and 100, we need to factor each number (factors of 12 = 1, 2, 3, 4, 6, 12; factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100) and choose the greatest factor that exactly divides both 12 and 100, i.e., 4.

How to Find the GCF of 12 and 100 by Long Division Method?

To find the GCF of 12, 100 using long division method, 100 is divided by 12. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

How to Find the GCF of 12 and 100 by Prime Factorization?

To find the GCF of 12 and 100, we will find the prime factorization of the given numbers, i.e. 12 = 2 × 2 × 3; 100 = 2 × 2 × 5 × 5.
⇒ Since 2, 2 are common terms in the prime factorization of 12 and 100. Hence, GCF(12, 100) = 2 × 2 = 4
☛ What is a Prime Number?

If the GCF of 100 and 12 is 4, Find its LCM.

GCF(100, 12) × LCM(100, 12) = 100 × 12
Since the GCF of 100 and 12 = 4
⇒ 4 × LCM(100, 12) = 1200
Therefore, LCM = 300
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 12, 100?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 12 and 100, i.e. GCF × LCM = 12 × 100.

What are the Methods to Find GCF of 12 and 100?

There are three commonly used methods to find the GCF of 12 and 100.

By Prime Factorization
By Listing Common Factors
By Long Division

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum