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HCF of 15 and 16

HCF of 15 and 16 is the largest possible number that divides 15 and 16 exactly without any remainder. The factors of 15 and 16 are 1, 3, 5, 15 and 1, 2, 4, 8, 16 respectively. There are 3 commonly used methods to find the HCF of 15 and 16 - Euclidean algorithm, prime factorization, and long division.

1.	HCF of 15 and 16
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 15 and 16?

Answer: HCF of 15 and 16 is 1.

Explanation:

The HCF of two non-zero integers, x(15) and y(16), is the highest positive integer m(1) that divides both x(15) and y(16) without any remainder.

Methods to Find HCF of 15 and 16

Let's look at the different methods for finding the HCF of 15 and 16.

Using Euclid's Algorithm
Long Division Method
Prime Factorization Method

HCF of 15 and 16 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.

Here X = 16 and Y = 15

HCF(16, 15) = HCF(15, 16 mod 15) = HCF(15, 1)
HCF(15, 1) = HCF(1, 15 mod 1) = HCF(1, 0)
HCF(1, 0) = 1 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 15 and 16 is 1.

HCF of 15 and 16 by Long Division

HCF of 15 and 16 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 16 (larger number) by 15 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (15) by the remainder (1).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the HCF of 15 and 16.

HCF of 15 and 16 by Prime Factorization

Prime factorization of 15 and 16 is (3 × 5) and (2 × 2 × 2 × 2) respectively. As visible, there are no common prime factors between 15 and 16, i.e. they are co-prime. Hence, the HCF of 15 and 16 will be 1.

☛ Also Check:

HCF of 15 and 16 Examples

Example 1: For two numbers, HCF = 1 and LCM = 240. If one number is 16, find the other number.

Solution:

Given: HCF (y, 16) = 1 and LCM (y, 16) = 240
∵ HCF × LCM = 16 × (y)
⇒ y = (HCF × LCM)/16
⇒ y = (1 × 240)/16
⇒ y = 15
Therefore, the other number is 15.
Example 2: Find the highest number that divides 15 and 16 exactly.

Solution:

The highest number that divides 15 and 16 exactly is their highest common factor, i.e. HCF of 15 and 16.
⇒ Factors of 15 and 16:
- Factors of 15 = 1, 3, 5, 15
- Factors of 16 = 1, 2, 4, 8, 16
Therefore, the HCF of 15 and 16 is 1.
Example 3: The product of two numbers is 240. If their HCF is 1, what is their LCM?

Solution:

Given: HCF = 1 and product of numbers = 240
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 240/1
Therefore, the LCM is 240.

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FAQs on HCF of 15 and 16

What is the HCF of 15 and 16?

The HCF of 15 and 16 is 1. To calculate the HCF (Highest Common Factor) of 15 and 16, we need to factor each number (factors of 15 = 1, 3, 5, 15; factors of 16 = 1, 2, 4, 8, 16) and choose the highest factor that exactly divides both 15 and 16, i.e., 1.

What is the Relation Between LCM and HCF of 15, 16?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 15 and 16, i.e. HCF × LCM = 15 × 16.

How to Find the HCF of 15 and 16 by Long Division Method?

To find the HCF of 15, 16 using long division method, 16 is divided by 15. The corresponding divisor (1) when remainder equals 0 is taken as HCF.

How to Find the HCF of 15 and 16 by Prime Factorization?

To find the HCF of 15 and 16, we will find the prime factorization of the given numbers, i.e. 15 = 3 × 5; 16 = 2 × 2 × 2 × 2.
⇒ There is no common prime factor for 15 and 16. Hence, HCF (15, 16) = 1.
☛ What is a Prime Number?

What are the Methods to Find HCF of 15 and 16?

There are three commonly used methods to find the HCF of 15 and 16.

By Euclidean Algorithm
By Prime Factorization
By Long Division

If the HCF of 16 and 15 is 1, Find its LCM.

HCF(16, 15) × LCM(16, 15) = 16 × 15
Since the HCF of 16 and 15 = 1
⇒ 1 × LCM(16, 15) = 240
Therefore, LCM = 240
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