Gcf Of 48 And 80

GCF of 48 and 80

GCF of 48 and 80 is the largest possible number that divides 48 and 80 exactly without whatsoever remainder. The factors of 48 and 80 are 1, 2, iii, 4, 6, viii, 12, 16, 24, 48 and 1, two, four, 5, 8, 10, xvi, twenty, twoscore, 80 respectively. There are iii commonly used methods to find the GCF of 48 and fourscore - prime factorization, long partitioning, and Euclidean algorithm.

1.	GCF of 48 and 80
2.	Listing of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 48 and lxxx?

Respond: GCF of 48 and 80 is 16.

Explanation:

The GCF of two non-zilch integers, 10(48) and y(80), is the greatest positive integer m(xvi) that divides both x(48) and y(80) without any residue.

Methods to Find GCF of 48 and 80

The methods to find the GCF of 48 and 80 are explained below.

• Prime Factorization Method
• Long Division Method
• Using Euclid's Algorithm

GCF of 48 and 80 by Prime Factorization

Prime factorization of 48 and lxxx is (two × 2 × ii × 2 × 3) and (ii × 2 × 2 × 2 × 5) respectively. As visible, 48 and 80 have mutual prime factors. Hence, the GCF of 48 and 80 is 2 × two × 2 × 2 = 16.

GCF of 48 and 80 past Long Division

GCF of 48 and eighty is the divisor that we get when the remainder becomes 0 after doing long sectionalization repeatedly.

• Step 1: Divide lxxx (larger number) by 48 (smaller number).
• Pace ii: Since the residue ≠ 0, we will carve up the divisor of footstep 1 (48) by the remainder (32).
• Step iii: Repeat this process until the remainder = 0.

The corresponding divisor (sixteen) is the GCF of 48 and 80.

GCF of 48 and 80 by Euclidean Algorithm

Every bit per the Euclidean Algorithm, GCF(Ten, Y) = GCF(Y, Ten mod Y)
where 10 > Y and mod is the modulo operator.

Here Ten = 80 and Y = 48

• GCF(80, 48) = GCF(48, eighty modernistic 48) = GCF(48, 32)
• GCF(48, 32) = GCF(32, 48 mod 32) = GCF(32, 16)
• GCF(32, 16) = GCF(16, 32 mod xvi) = GCF(16, 0)
• GCF(16, 0) = 16 (∵ GCF(10, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 48 and fourscore is sixteen.

☛ Also Check:

• GCF of 26 and 14 = two
• GCF of 12 and 14 = 2
• GCF of eleven and 44 = 11
• GCF of 24 and 80 = 8
• GCF of 24 and 56 = eight
• GCF of 21 and 24 = 3
• GCF of 20 and 45 = five

GCF of 48 and 80 Examples

1. Instance 1: Find the greatest number that divides 48 and fourscore exactly.

   Solution:

   The greatest number that divides 48 and 80 exactly is their greatest common cistron, i.east. GCF of 48 and 80.
   ⇒ Factors of 48 and lxxx:

   • Factors of 48 = 1, 2, 3, iv, 6, eight, 12, 16, 24, 48
   • Factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

   Therefore, the GCF of 48 and fourscore is 16.

2. Example 2: For two numbers, GCF = 16 and LCM = 240. If one number is 48, notice the other number.

   Solution:

   Given: GCF (y, 48) = 16 and LCM (y, 48) = 240
   ∵ GCF × LCM = 48 × (y)
   ⇒ y = (GCF × LCM)/48
   ⇒ y = (16 × 240)/48
   ⇒ y = 80
   Therefore, the other number is 80.

3. Example 3: The product of two numbers is 3840. If their GCF is 16, what is their LCM?

   Solution:

   Given: GCF = 16 and product of numbers = 3840
   ∵ LCM × GCF = product of numbers
   ⇒ LCM = Production/GCF = 3840/16
   Therefore, the LCM is 240.

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FAQs on GCF of 48 and lxxx

What is the GCF of 48 and 80?

The GCF of 48 and eighty is 16 . To summate the GCF of 48 and eighty, nosotros need to gene each number (factors of 48 = i, 2, 3, 4, 6, viii, 12, xvi, 24, 48; factors of 80 = i, 2, 4, 5, 8, 10, 16, twenty, 40, 80) and cull the greatest factor that exactly divides both 48 and 80, i.e., sixteen.

How to Detect the GCF of 48 and lxxx by Long Partition Method?

To detect the GCF of 48, fourscore using long sectionalization method, fourscore is divided past 48. The corresponding divisor (sixteen) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 48, eighty?

The following equation can be used to limited the relation between Least Common Multiple and GCF of 48 and 80, i.eastward. GCF × LCM = 48 × eighty.

How to Find the GCF of 48 and 80 by Prime number Factorization?

To find the GCF of 48 and 80, we volition find the prime factorization of the given numbers, i.e. 48 = ii × two × 2 × 2 × 3; 80 = 2 × 2 × ii × 2 × five.
⇒ Since 2, ii, 2, 2 are common terms in the prime number factorization of 48 and 80. Hence, GCF(48, fourscore) = ii × 2 × 2 × 2 = xvi
☛ Prime number Number

If the GCF of 80 and 48 is sixteen, Find its LCM.

GCF(80, 48) × LCM(80, 48) = 80 × 48
Since the GCF of 80 and 48 = 16
⇒ 16 × LCM(80, 48) = 3840
Therefore, LCM = 240
☛ Greatest Common Factor Calculator

What are the Methods to Find GCF of 48 and fourscore?

There are three commonly used methods to find the GCF of 48 and eighty.

• By Long Division
• Past Euclidean Algorithm
• By Prime Factorization

Gcf Of 48 And 80,

Source: https://www.cuemath.com/numbers/gcf-of-48-and-80/

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