Gcf Of 24 And 60

GCF of 24 and 60

GCF of 24 and 60 is the largest possible number that divides 24 and lx exactly without any remainder. The factors of 24 and 60 are one, 2, 3, 4, six, 8, 12, 24 and i, ii, 3, 4, 5, 6, ten, 12, 15, 20, xxx, 60 respectively. There are 3 normally used methods to discover the GCF of 24 and 60 - Euclidean algorithm, long sectionalisation, and prime number factorization.

1.	GCF of 24 and 60
2.	Listing of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 24 and 60?

Respond: GCF of 24 and threescore is 12.

Caption:

The GCF of two non-cipher integers, x(24) and y(sixty), is the greatest positive integer g(12) that divides both x(24) and y(lx) without any remainder.

Methods to Find GCF of 24 and lx

Let'south look at the different methods for finding the GCF of 24 and 60.

• Long Segmentation Method
• Prime number Factorization Method
• Listing Mutual Factors

GCF of 24 and 60 past Long Segmentation

GCF of 24 and 60 is the divisor that nosotros get when the remainder becomes 0 after doing long division repeatedly.

• Step 1: Divide 60 (larger number) by 24 (smaller number).
• Step 2: Since the remainder ≠ 0, we volition dissever the divisor of footstep one (24) by the remainder (12).
• Step 3: Repeat this process until the residual = 0.

The corresponding divisor (12) is the GCF of 24 and 60.

GCF of 24 and 60 by Prime Factorization

Prime factorization of 24 and 60 is (2 × ii × 2 × three) and (2 × 2 × 3 × 5) respectively. As visible, 24 and 60 have mutual prime factors. Hence, the GCF of 24 and lx is 2 × two × three = 12.

GCF of 24 and 60 past Listing Common Factors

• Factors of 24: one, 2, 3, 4, 6, 8, 12, 24
• Factors of 60: 1, 2, 3, four, 5, 6, ten, 12, 15, 20, 30, 60

There are six common factors of 24 and sixty, that are i, 2, three, iv, 6, and 12. Therefore, the greatest common factor of 24 and sixty is 12.

☛ Also Check:

• GCF of 84 and 108 = 12
• GCF of xiv and 24 = 2
• GCF of 32 and 80 = 16
• GCF of ix and 36 = nine
• GCF of 8 and 10 = two
• GCF of 92 and 23 = 23
• GCF of 18 and 48 = vi

GCF of 24 and 60 Examples

1. Example 1: Find the GCF of 24 and lx, if their LCM is 120.

   Solution:

   ∵ LCM × GCF = 24 × lx
   ⇒ GCF(24, 60) = (24 × sixty)/120 = 12
   Therefore, the greatest common cistron of 24 and 60 is 12.

2. Instance ii: For 2 numbers, GCF = 12 and LCM = 120. If one number is 60, find the other number.

   Solution:

   Given: GCF (y, 60) = 12 and LCM (y, threescore) = 120
   ∵ GCF × LCM = 60 × (y)
   ⇒ y = (GCF × LCM)/sixty
   ⇒ y = (12 × 120)/60
   ⇒ y = 24
   Therefore, the other number is 24.

3. Example 3: The product of ii numbers is 1440. If their GCF is 12, what is their LCM?

   Solution:

   Given: GCF = 12 and production of numbers = 1440
   ∵ LCM × GCF = production of numbers
   ⇒ LCM = Product/GCF = 1440/12
   Therefore, the LCM is 120.

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FAQs on GCF of 24 and lx

What is the GCF of 24 and 60?

The GCF of 24 and 60 is 12 . To calculate the greatest common factor (GCF) of 24 and 60, we demand to factor each number (factors of 24 = 1, 2, iii, four, 6, 8, 12, 24; factors of lx = 1, 2, 3, 4, 5, vi, 10, 12, 15, 20, 30, 60) and cull the greatest cistron that exactly divides both 24 and sixty, i.due east., 12.

How to Find the GCF of 24 and lx by Long Division Method?

To observe the GCF of 24, 60 using long partition method, 60 is divided by 24. The corresponding divisor (12) when remainder equals 0 is taken every bit GCF.

What are the Methods to Find GCF of 24 and 60?

At that place are three commonly used methods to discover the GCF of 24 and 60.

• By Long Division
• By Listing Common Factors
• By Prime number Factorization

If the GCF of 60 and 24 is 12, Find its LCM.

GCF(sixty, 24) × LCM(60, 24) = 60 × 24
Since the GCF of 60 and 24 = 12
⇒ 12 × LCM(sixty, 24) = 1440
Therefore, LCM = 120
☛ GCF Calculator

What is the Relation Between LCM and GCF of 24, 60?

The following equation can exist used to express the relation between LCM (Least Common Multiple) and GCF of 24 and 60, i.e. GCF × LCM = 24 × 60.

How to Notice the GCF of 24 and 60 by Prime Factorization?

To find the GCF of 24 and sixty, we will find the prime factorization of the given numbers, i.due east. 24 = 2 × 2 × 2 × 3; 60 = 2 × 2 × 3 × 5.
⇒ Since 2, 2, 3 are mutual terms in the prime factorization of 24 and 60. Hence, GCF(24, lx) = ii × ii × three = 12
☛ Prime Number

Gcf Of 24 And 60,

Source: https://www.cuemath.com/numbers/gcf-of-24-and-60/

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