Highest Common Factor of 697, 417, 523, 354 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 697, 417, 523, 354 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 697, 417, 523, 354 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 697, 417, 523, 354 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 697, 417, 523, 354 is 1.

HCF(697, 417, 523, 354) = 1

HCF of 697, 417, 523, 354 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 697, 417, 523, 354 is 1.

Highest Common Factor of 697,417,523,354 using Euclid's algorithm

Highest Common Factor of 697,417,523,354 is 1

Step 1: Since 697 > 417, we apply the division lemma to 697 and 417, to get

697 = 417 x 1 + 280

Step 2: Since the reminder 417 ≠ 0, we apply division lemma to 280 and 417, to get

417 = 280 x 1 + 137

Step 3: We consider the new divisor 280 and the new remainder 137, and apply the division lemma to get

280 = 137 x 2 + 6

We consider the new divisor 137 and the new remainder 6,and apply the division lemma to get

137 = 6 x 22 + 5

We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get

6 = 5 x 1 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 697 and 417 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(137,6) = HCF(280,137) = HCF(417,280) = HCF(697,417) .

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

Step 1: Since 523 > 1, we apply the division lemma to 523 and 1, to get

523 = 1 x 523 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 523 is 1

Notice that 1 = HCF(523,1) .

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

Step 1: Since 354 > 1, we apply the division lemma to 354 and 1, to get

354 = 1 x 354 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 354 is 1

Notice that 1 = HCF(354,1) .

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Frequently Asked Questions on HCF of 697, 417, 523, 354 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 697, 417, 523, 354?

Answer: HCF of 697, 417, 523, 354 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 697, 417, 523, 354 using Euclid's Algorithm?

Answer: For arbitrary numbers 697, 417, 523, 354 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.