Highest Common Factor of 670, 898, 652 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 670, 898, 652 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 670, 898, 652 is 2 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 670, 898, 652 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 670, 898, 652 is 2.

HCF(670, 898, 652) = 2

HCF of 670, 898, 652 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 670, 898, 652 is 2.

Highest Common Factor of 670,898,652 using Euclid's algorithm

Highest Common Factor of 670,898,652 is 2

Step 1: Since 898 > 670, we apply the division lemma to 898 and 670, to get

898 = 670 x 1 + 228

Step 2: Since the reminder 670 ≠ 0, we apply division lemma to 228 and 670, to get

670 = 228 x 2 + 214

Step 3: We consider the new divisor 228 and the new remainder 214, and apply the division lemma to get

228 = 214 x 1 + 14

We consider the new divisor 214 and the new remainder 14,and apply the division lemma to get

214 = 14 x 15 + 4

We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get

14 = 4 x 3 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 670 and 898 is 2

Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(214,14) = HCF(228,214) = HCF(670,228) = HCF(898,670) .

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

Step 1: Since 652 > 2, we apply the division lemma to 652 and 2, to get

652 = 2 x 326 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 652 is 2

Notice that 2 = HCF(652,2) .

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Frequently Asked Questions on HCF of 670, 898, 652 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 670, 898, 652?

Answer: HCF of 670, 898, 652 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 670, 898, 652 using Euclid's Algorithm?

Answer: For arbitrary numbers 670, 898, 652 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.