Highest Common Factor of 362, 662, 557 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 362, 662, 557 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 362, 662, 557 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 362, 662, 557 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 362, 662, 557 is 1.

HCF(362, 662, 557) = 1

HCF of 362, 662, 557 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 362, 662, 557 is 1.

Highest Common Factor of 362,662,557 using Euclid's algorithm

Highest Common Factor of 362,662,557 is 1

Step 1: Since 662 > 362, we apply the division lemma to 662 and 362, to get

662 = 362 x 1 + 300

Step 2: Since the reminder 362 ≠ 0, we apply division lemma to 300 and 362, to get

362 = 300 x 1 + 62

Step 3: We consider the new divisor 300 and the new remainder 62, and apply the division lemma to get

300 = 62 x 4 + 52

We consider the new divisor 62 and the new remainder 52,and apply the division lemma to get

62 = 52 x 1 + 10

We consider the new divisor 52 and the new remainder 10,and apply the division lemma to get

52 = 10 x 5 + 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 362 and 662 is 2

Notice that 2 = HCF(10,2) = HCF(52,10) = HCF(62,52) = HCF(300,62) = HCF(362,300) = HCF(662,362) .

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

Step 1: Since 557 > 2, we apply the division lemma to 557 and 2, to get

557 = 2 x 278 + 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 557 is 1

Notice that 1 = HCF(2,1) = HCF(557,2) .

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Frequently Asked Questions on HCF of 362, 662, 557 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 362, 662, 557?

Answer: HCF of 362, 662, 557 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 362, 662, 557 using Euclid's Algorithm?

Answer: For arbitrary numbers 362, 662, 557 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.