Highest Common Factor of 242, 442, 505 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 242, 442, 505 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 242, 442, 505 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 242, 442, 505 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 242, 442, 505 is 1.

HCF(242, 442, 505) = 1

HCF of 242, 442, 505 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 242, 442, 505 is 1.

Highest Common Factor of 242,442,505 using Euclid's algorithm

Highest Common Factor of 242,442,505 is 1

Step 1: Since 442 > 242, we apply the division lemma to 442 and 242, to get

442 = 242 x 1 + 200

Step 2: Since the reminder 242 ≠ 0, we apply division lemma to 200 and 242, to get

242 = 200 x 1 + 42

Step 3: We consider the new divisor 200 and the new remainder 42, and apply the division lemma to get

200 = 42 x 4 + 32

We consider the new divisor 42 and the new remainder 32,and apply the division lemma to get

42 = 32 x 1 + 10

We consider the new divisor 32 and the new remainder 10,and apply the division lemma to get

32 = 10 x 3 + 2

We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get

10 = 2 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 242 and 442 is 2

Notice that 2 = HCF(10,2) = HCF(32,10) = HCF(42,32) = HCF(200,42) = HCF(242,200) = HCF(442,242) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 505 > 2, we apply the division lemma to 505 and 2, to get

505 = 2 x 252 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 505 is 1

Notice that 1 = HCF(2,1) = HCF(505,2) .

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Frequently Asked Questions on HCF of 242, 442, 505 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 242, 442, 505?

Answer: HCF of 242, 442, 505 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 242, 442, 505 using Euclid's Algorithm?

Answer: For arbitrary numbers 242, 442, 505 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.