Gcf Of 120 And 36

GCF of 120 and 36

GCF of 120 and 36 is the largest possible number that divides 120 and 36 exactly without any remainder. The factors of 120 and 36 are i, 2, three, 4, 5, half-dozen, 8, 10, 12, xv, twenty, 24, 30, 40, 60, 120 and 1, two, 3, 4, 6, ix, 12, 18, 36 respectively. At that place are 3 normally used methods to find the GCF of 120 and 36 - Euclidean algorithm, prime number factorization, and long partition.

one.	GCF of 120 and 36
2.	List of Methods
three.	Solved Examples
4.	FAQs

What is GCF of 120 and 36?

Reply: GCF of 120 and 36 is 12.

GCF of 120 and 36

Explanation:

The GCF of two not-zippo integers, x(120) and y(36), is the greatest positive integer m(12) that divides both ten(120) and y(36) without any remainder.

Methods to Find GCF of 120 and 36

Let'due south look at the different methods for finding the GCF of 120 and 36.

Using Euclid'due south Algorithm
Listing Common Factors
Long Division Method

GCF of 120 and 36 past Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, 10 modernistic Y)
where X > Y and modernistic is the modulo operator.

Here X = 120 and Y = 36

GCF(120, 36) = GCF(36, 120 modernistic 36) = GCF(36, 12)
GCF(36, 12) = GCF(12, 36 modern 12) = GCF(12, 0)
GCF(12, 0) = 12 (∵ GCF(10, 0) = |X|, where Ten ≠ 0)

Therefore, the value of GCF of 120 and 36 is 12.

GCF of 120 and 36 by List Mutual Factors

Factors of 120: ane, ii, three, 4, five, vi, 8, 10, 12, xv, 20, 24, 30, 40, 60, 120
Factors of 36: ane, 2, 3, iv, 6, 9, 12, xviii, 36

In that location are vi common factors of 120 and 36, that are one, 2, three, 4, 6, and 12. Therefore, the greatest mutual gene of 120 and 36 is 12.

GCF of 120 and 36 by Long Division

GCF of 120 and 36 is the divisor that we get when the residuum becomes 0 after doing long division repeatedly.

Step 1: Divide 120 (larger number) by 36 (smaller number).
Step 2: Since the remainder ≠ 0, nosotros volition divide the divisor of step ane (36) by the rest (12).
Stride iii: Repeat this process until the remainder = 0.

The corresponding divisor (12) is the GCF of 120 and 36.

☛ As well Check:

GCF of 72 and 84 = 12
GCF of 9 and 27 = 9
GCF of 28 and 30 = 2
GCF of 26 and 14 = 2
GCF of nine and 16 = one
GCF of 25 and 30 = 5
GCF of 33 and 44 = 11

GCF of 120 and 36 Examples

Example 1: Find the GCF of 120 and 36, if their LCM is 360.

Solution:

∵ LCM × GCF = 120 × 36
⇒ GCF(120, 36) = (120 × 36)/360 = 12
Therefore, the greatest common factor of 120 and 36 is 12.
Example 2: For two numbers, GCF = 12 and LCM = 360. If one number is 120, find the other number.

Solution:

Given: GCF (z, 120) = 12 and LCM (z, 120) = 360
∵ GCF × LCM = 120 × (z)
⇒ z = (GCF × LCM)/120
⇒ z = (12 × 360)/120
⇒ z = 36
Therefore, the other number is 36.
Instance 3: Observe the greatest number that divides 120 and 36 exactly.

Solution:

The greatest number that divides 120 and 36 exactly is their greatest common cistron, i.e. GCF of 120 and 36.
⇒ Factors of 120 and 36:
- Factors of 120 = 1, 2, 3, 4, five, 6, 8, 10, 12, 15, twenty, 24, 30, 40, 60, 120
- Factors of 36 = one, two, three, four, 6, 9, 12, 18, 36
Therefore, the GCF of 120 and 36 is 12.

get to slidego to slidego to slide

Gear up to see the world through math's eyes?

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

Book a Free Trial Class

FAQs on GCF of 120 and 36

What is the GCF of 120 and 36?

The GCF of 120 and 36 is 12 . To calculate the greatest common gene (GCF) of 120 and 36, we demand to factor each number (factors of 120 = 1, ii, three, four, 5, 6, 8, x, 12, fifteen, 20, 24, 30, twoscore, lx, 120; factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36) and choose the greatest factor that exactly divides both 120 and 36, i.e., 12.

What is the Relation Betwixt LCM and GCF of 120, 36?

The following equation tin be used to limited the relation between Least Common Multiple and GCF of 120 and 36, i.eastward. GCF × LCM = 120 × 36.

What are the Methods to Find GCF of 120 and 36?

There are iii ordinarily used methods to find the GCF of 120 and 36.

By Euclidean Algorithm
By Prime number Factorization
By Long Division

If the GCF of 36 and 120 is 12, Find its LCM.

GCF(36, 120) × LCM(36, 120) = 36 × 120
Since the GCF of 36 and 120 = 12
⇒ 12 × LCM(36, 120) = 4320
Therefore, LCM = 360
☛ GCF Estimator

How to Find the GCF of 120 and 36 by Long Partition Method?

To notice the GCF of 120, 36 using long division method, 120 is divided by 36. The respective divisor (12) when remainder equals 0 is taken as GCF.

How to Discover the GCF of 120 and 36 by Prime Factorization?

To find the GCF of 120 and 36, we will detect the prime factorization of the given numbers, i.eastward. 120 = 2 × 2 × 2 × iii × 5; 36 = 2 × 2 × 3 × three.
⇒ Since ii, 2, three are common terms in the prime factorization of 120 and 36. Hence, GCF(120, 36) = 2 × 2 × 3 = 12
☛ What are Prime Numbers?