Highest Common Factor of 698, 918, 407 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 698, 918, 407 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 698, 918, 407 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 698, 918, 407 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 698, 918, 407 is 1.

HCF(698, 918, 407) = 1

HCF of 698, 918, 407 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 698, 918, 407 is 1.

Highest Common Factor of 698,918,407 using Euclid's algorithm

Highest Common Factor of 698,918,407 is 1

Step 1: Since 918 > 698, we apply the division lemma to 918 and 698, to get

918 = 698 x 1 + 220

Step 2: Since the reminder 698 ≠ 0, we apply division lemma to 220 and 698, to get

698 = 220 x 3 + 38

Step 3: We consider the new divisor 220 and the new remainder 38, and apply the division lemma to get

220 = 38 x 5 + 30

We consider the new divisor 38 and the new remainder 30,and apply the division lemma to get

38 = 30 x 1 + 8

We consider the new divisor 30 and the new remainder 8,and apply the division lemma to get

30 = 8 x 3 + 6

We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get

8 = 6 x 1 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 698 and 918 is 2

Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(30,8) = HCF(38,30) = HCF(220,38) = HCF(698,220) = HCF(918,698) .

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

Step 1: Since 407 > 2, we apply the division lemma to 407 and 2, to get

407 = 2 x 203 + 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 407 is 1

Notice that 1 = HCF(2,1) = HCF(407,2) .

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Frequently Asked Questions on HCF of 698, 918, 407 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 698, 918, 407?

Answer: HCF of 698, 918, 407 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 698, 918, 407 using Euclid's Algorithm?

Answer: For arbitrary numbers 698, 918, 407 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.