Math, asked by drndtippeswamy, 7 days ago

HCF OF 14,2434 Full Sentence​

Answers

Answered by alagappanalagappan19
1

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Answered by abishahari2020
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Answer:

Let's look at the different methods for finding the HCF of 14 and 21.

Long Division Method

Prime Factorization Method

Using Euclid's Algorithm

HCF of 14 and 21 by Long Division

HCF of 14 and 21 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 21 (larger number) by 14 (smaller number).

Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (14) by the remainder (7).

Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (7) is the HCF of 14 and 21.

HCF of 14 and 21 by Prime Factorization

HCF of 14 and 21 by Prime Factorization

Prime factorization of 14 and 21 is (2 × 7) and (3 × 7) respectively. As visible, 14 and 21 have only one common prime factor i.e. 7. Hence, the HCF of 14 and 21 is 7.

HCF of 14 and 21 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 = 21 and Y = 14

HCF(21, 14) = HCF(14, 21 mod 14) = HCF(14, 7)

HCF(14, 7) = HCF(7, 14 mod 7) = HCF(7, 0)

HCF(7, 0) = 7 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 14 and 21 is 7.

☛ Also Check:

HCF of 12, 45 and 75 = 3

HCF of 27 and 45 = 9

HCF of 15 and 18 = 3

HCF of 144 and 192 = 48

HCF of 150 and 225 = 75

HCF of 70, 105 and 175 = 35

HCF of 18, 54 and 81 = 9

HCF of 14 and 21 Examples

Example 1: For two numbers, HCF = 7 and LCM = 42. If one number is 21, find the other number.

Solution:

Given: HCF (z, 21) = 7 and LCM (z, 21) = 42

∵ HCF × LCM = 21 × (z)

⇒ z = (HCF × LCM)/21

⇒ z = (7 × 42)/21

⇒ z = 14

Therefore, the other number is 14.

Example 2: The product of two numbers is 294. If their HCF is 7, what is their LCM?

Solution:

Given: HCF = 7 and product of numbers = 294

∵ LCM × HCF = product of numbers

⇒ LCM = Product/HCF = 294/7

Therefore, the LCM is 42.

Example 3: Find the HCF of 14 and 21, if their LCM is 42.

Solution:

∵ LCM × HCF = 14 × 21

⇒ HCF(14, 21) = (14 × 21)/42 = 7

Therefore, the highest common factor of 14 and 21 is 7.

If the HCF of 21 and 14 is 7, Find its LCM.

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