Highest Common Factor of 870, 335, 398 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 870, 335, 398 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 870, 335, 398 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 870, 335, 398 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 870, 335, 398 is 1.

HCF(870, 335, 398) = 1

HCF of 870, 335, 398 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 870, 335, 398 is 1.

Highest Common Factor of 870,335,398 using Euclid's algorithm

Highest Common Factor of 870,335,398 is 1

Step 1: Since 870 > 335, we apply the division lemma to 870 and 335, to get

870 = 335 x 2 + 200

Step 2: Since the reminder 335 ≠ 0, we apply division lemma to 200 and 335, to get

335 = 200 x 1 + 135

Step 3: We consider the new divisor 200 and the new remainder 135, and apply the division lemma to get

200 = 135 x 1 + 65

We consider the new divisor 135 and the new remainder 65,and apply the division lemma to get

135 = 65 x 2 + 5

We consider the new divisor 65 and the new remainder 5,and apply the division lemma to get

65 = 5 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 870 and 335 is 5

Notice that 5 = HCF(65,5) = HCF(135,65) = HCF(200,135) = HCF(335,200) = HCF(870,335) .

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

Step 1: Since 398 > 5, we apply the division lemma to 398 and 5, to get

398 = 5 x 79 + 3

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get

5 = 3 x 1 + 2

Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 5 and 398 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(398,5) .

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Frequently Asked Questions on HCF of 870, 335, 398 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 870, 335, 398?

Answer: HCF of 870, 335, 398 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 870, 335, 398 using Euclid's Algorithm?

Answer: For arbitrary numbers 870, 335, 398 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.