Gcf Of 64 And 28

GCF of 28 and 64

GCF of 28 and 64 is the largest possible number that divides 28 and 64 exactly without any remainder. The factors of 28 and 64 are 1, two, 4, 7, xiv, 28 and i, 2, 4, viii, xvi, 32, 64 respectively. There are iii commonly used methods to observe the GCF of 28 and 64 - long partition, prime factorization, and Euclidean algorithm.

i.	GCF of 28 and 64
2.	List of Methods
iii.	Solved Examples
4.	FAQs

What is GCF of 28 and 64?

Answer: GCF of 28 and 64 is 4.

Explanation:

The GCF of 2 non-goose egg integers, ten(28) and y(64), is the greatest positive integer grand(4) that divides both x(28) and y(64) without any remainder.

Methods to Detect GCF of 28 and 64

The methods to detect the GCF of 28 and 64 are explained below.

• Listing Common Factors
• Long Division Method
• Prime Factorization Method

GCF of 28 and 64 past Listing Common Factors

• Factors of 28: ane, 2, four, 7, 14, 28
• Factors of 64: 1, ii, 4, 8, xvi, 32, 64

There are 3 common factors of 28 and 64, that are 1, two, and 4. Therefore, the greatest mutual factor of 28 and 64 is 4.

GCF of 28 and 64 by Long Division

GCF of 28 and 64 is the divisor that we become when the residue becomes 0 after doing long division repeatedly.

• Step 1: Divide 64 (larger number) by 28 (smaller number).
• Stride 2: Since the remainder ≠ 0, we volition separate the divisor of step 1 (28) past the residual (8).
• Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (four) is the GCF of 28 and 64.

GCF of 28 and 64 by Prime number Factorization

Prime factorization of 28 and 64 is (2 × 2 × seven) and (2 × 2 × ii × two × 2 × ii) respectively. As visible, 28 and 64 have common prime factors. Hence, the GCF of 28 and 64 is 2 × 2 = 4.

☛ Also Check:

• GCF of 22 and 33 = eleven
• GCF of 25 and lx = v
• GCF of 21 and 35 = seven
• GCF of 60 and 84 = 12
• GCF of 56 and 49 = 7
• GCF of 25 and ninety = 5
• GCF of 56 and 72 = 8

GCF of 28 and 64 Examples

1. Example one: Observe the greatest number that divides 28 and 64 exactly.

   Solution:

   The greatest number that divides 28 and 64 exactly is their greatest common factor, i.due east. GCF of 28 and 64.
   ⇒ Factors of 28 and 64:

   • Factors of 28 = one, ii, four, 7, 14, 28
   • Factors of 64 = 1, ii, 4, eight, 16, 32, 64

   Therefore, the GCF of 28 and 64 is iv.

2. Instance 2: The product of 2 numbers is 1792. If their GCF is 4, what is their LCM?

   Solution:

   Given: GCF = four and product of numbers = 1792
   ∵ LCM × GCF = production of numbers
   ⇒ LCM = Product/GCF = 1792/4
   Therefore, the LCM is 448.

3. Example 3: For 2 numbers, GCF = 4 and LCM = 448. If ane number is 64, find the other number.

   Solution:

   Given: GCF (z, 64) = 4 and LCM (z, 64) = 448
   ∵ GCF × LCM = 64 × (z)
   ⇒ z = (GCF × LCM)/64
   ⇒ z = (4 × 448)/64
   ⇒ z = 28
   Therefore, the other number is 28.

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FAQs on GCF of 28 and 64

What is the GCF of 28 and 64?

The GCF of 28 and 64 is iv . To summate the GCF (Greatest Common Gene) of 28 and 64, nosotros demand to gene each number (factors of 28 = 1, 2, 4, 7, 14, 28; factors of 64 = one, ii, iv, 8, 16, 32, 64) and cull the greatest cistron that exactly divides both 28 and 64, i.e., four.

If the GCF of 64 and 28 is 4, Notice its LCM.

GCF(64, 28) × LCM(64, 28) = 64 × 28
Since the GCF of 64 and 28 = iv
⇒ 4 × LCM(64, 28) = 1792
Therefore, LCM = 448
☛ GCF Calculator

How to Discover the GCF of 28 and 64 by Long Partitioning Method?

To observe the GCF of 28, 64 using long division method, 64 is divided by 28. The corresponding divisor (4) when residual equals 0 is taken as GCF.

What are the Methods to Find GCF of 28 and 64?

At that place are iii commonly used methods to find the GCF of 28 and 64.

• By Listing Mutual Factors
• By Long Sectionalisation
• By Prime number Factorization

What is the Relation Between LCM and GCF of 28, 64?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 28 and 64, i.e. GCF × LCM = 28 × 64.

How to Find the GCF of 28 and 64 by Prime Factorization?

To find the GCF of 28 and 64, nosotros volition discover the prime factorization of the given numbers, i.e. 28 = 2 × two × 7; 64 = ii × 2 × 2 × 2 × 2 × 2.
⇒ Since 2, two are mutual terms in the prime factorization of 28 and 64. Hence, GCF(28, 64) = 2 × 2 = 4
☛ What is a Prime Number?

Gcf Of 64 And 28,

Source: https://www.cuemath.com/numbers/gcf-of-28-and-64/

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