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HCF of 12, 16 and 28

HCF of 12, 16 and 28 is the largest possible number that divides 12, 16 and 28 exactly without any remainder. The factors of 12, 16 and 28 are (1, 2, 3, 4, 6, 12), (1, 2, 4, 8, 16) and (1, 2, 4, 7, 14, 28) respectively. There are 3 commonly used methods to find the HCF of 12, 16 and 28 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 12, 16 and 28
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 12, 16 and 28?

Answer: HCF of 12, 16 and 28 is 4.

Explanation:

The HCF of three non-zero integers, x(12), y(16) and z(28), is the highest positive integer m(4) that divides x(12), y(16) and z(28) without any remainder.

Methods to Find HCF of 12, 16 and 28

The methods to find the HCF of 12, 16 and 28 are explained below.

Long Division Method
Prime Factorization Method
Using Euclid's Algorithm

HCF of 12, 16 and 28 by Long Division

HCF of 12, 16 and 28 can be represented as HCF of (HCF of 12, 16) and 28. HCF(12, 16, 28) can be thus calculated by first finding HCF(12, 16) using long division and thereafter using this result with 28 to perform long division again.

Step 1: Divide 16 (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). Repeat this process until the remainder = 0.
⇒ HCF(12, 16) = 4.
Step 3: Now to find the HCF of 4 and 28, we will perform a long division on 28 and 4.
Step 4: For remainder = 0, divisor = 4 ⇒ HCF(4, 28) = 4

Thus, HCF(12, 16, 28) = HCF(HCF(12, 16), 28) = 4.

HCF of 12, 16 and 28 by Prime Factorization

Prime factorization of 12, 16 and 28 is (2 × 2 × 3), (2 × 2 × 2 × 2) and (2 × 2 × 7) respectively. As visible, 12, 16 and 28 have common prime factors. Hence, the HCF of 12, 16 and 28 is 2 × 2 = 4.

HCF of 12, 16 and 28 by Euclidean Algorithm

As per the Euclidean Algorithm, HCF(X, Y) = HCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

HCF(12, 16, 28) = HCF(HCF(12, 16), 28)

HCF(16, 12) = HCF(12, 16 mod 12) = HCF(12, 4)
HCF(12, 4) = HCF(4, 12 mod 4) = HCF(4, 0)
HCF(4, 0) = 4 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Steps for HCF(4, 28)

HCF(28, 4) = HCF(4, 28 mod 4) = HCF(4, 0)
HCF(4, 0) = 4 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 12, 16 and 28 is 4.

☛ Also Check:

HCF of 12, 16 and 28 Examples

Example 1: Calculate the HCF of 12, 16, and 28 using LCM of the given numbers.

Solution:

Prime factorization of 12, 16 and 28 is given as,
- 12 = 2 × 2 × 3
- 16 = 2 × 2 × 2 × 2
- 28 = 2 × 2 × 7
LCM(12, 16) = 48, LCM(16, 28) = 112, LCM(28, 12) = 84, LCM(12, 16, 28) = 336
⇒ HCF(12, 16, 28) = [(12 × 16 × 28) × LCM(12, 16, 28)]/[LCM(12, 16) × LCM (16, 28) × LCM(28, 12)]
⇒ HCF(12, 16, 28) = (5376 × 336)/(48 × 112 × 84)
⇒ HCF(12, 16, 28) = 4.
Therefore, the HCF of 12, 16 and 28 is 4.
Example 2: Find the highest number that divides 12, 16, and 28 completely.

Solution:

The highest number that divides 12, 16, and 28 exactly is their highest common factor.
- Factors of 12 = 1, 2, 3, 4, 6, 12
- Factors of 16 = 1, 2, 4, 8, 16
- Factors of 28 = 1, 2, 4, 7, 14, 28
The HCF of 12, 16, and 28 is 4.
∴ The highest number that divides 12, 16, and 28 is 4.
Example 3: Verify the relation between the LCM and HCF of 12, 16 and 28.

Solution:

The relation between the LCM and HCF of 12, 16 and 28 is given as, HCF(12, 16, 28) = [(12 × 16 × 28) × LCM(12, 16, 28)]/[LCM(12, 16) × LCM (16, 28) × LCM(12, 28)]
⇒ Prime factorization of 12, 16 and 28:
- 12 = 2 × 2 × 3
- 16 = 2 × 2 × 2 × 2
- 28 = 2 × 2 × 7
∴ LCM of (12, 16), (16, 28), (12, 28), and (12, 16, 28) is 48, 112, 84, and 336 respectively.
Now, LHS = HCF(12, 16, 28) = 4.
And, RHS = [(12 × 16 × 28) × LCM(12, 16, 28)]/[LCM(12, 16) × LCM (16, 28) × LCM(12, 28)] = [(5376) × 336]/[48 × 112 × 84]
LHS = RHS = 4.
Hence verified.

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FAQs on HCF of 12, 16 and 28

What is the HCF of 12, 16 and 28?

The HCF of 12, 16 and 28 is 4. To calculate the highest common factor (HCF) of 12, 16 and 28, we need to factor each number (factors of 12 = 1, 2, 3, 4, 6, 12; factors of 16 = 1, 2, 4, 8, 16; factors of 28 = 1, 2, 4, 7, 14, 28) and choose the highest factor that exactly divides 12, 16 and 28, i.e., 4.

How to Find the HCF of 12, 16 and 28 by Prime Factorization?

To find the HCF of 12, 16 and 28, we will find the prime factorization of given numbers, i.e. 12 = 2 × 2 × 3; 16 = 2 × 2 × 2 × 2; 28 = 2 × 2 × 7.
⇒ Since 2, 2 are common terms in the prime factorization of 12, 16 and 28. Hence, HCF(12, 16, 28) = 2 × 2 = 4
☛ What is a Prime Number?

What is the Relation Between LCM and HCF of 12, 16 and 28?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 12, 16 and 28, i.e. HCF(12, 16, 28) = [(12 × 16 × 28) × LCM(12, 16, 28)]/[LCM(12, 16) × LCM (16, 28) × LCM(12, 28)].
☛ Highest Common Factor Calculator

What are the Methods to Find HCF of 12, 16 and 28?

There are three commonly used methods to find the HCF of 12, 16 and 28.

By Long Division
By Listing Common Factors
By Prime Factorization

Which of the following is HCF of 12, 16 and 28? 4, 58, 63, 49, 74, 68, 42, 43

HCF of 12, 16, 28 will be the number that divides 12, 16, and 28 without leaving any remainder. The only number that satisfies the given condition is 4.

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