Highest Common Factor of 694, 288, 138 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 694, 288, 138 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 694, 288, 138 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 694, 288, 138 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 694, 288, 138 is 2.

HCF(694, 288, 138) = 2

HCF of 694, 288, 138 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 694, 288, 138 is 2.

Highest Common Factor of 694,288,138 using Euclid's algorithm

Highest Common Factor of 694,288,138 is 2

Step 1: Since 694 > 288, we apply the division lemma to 694 and 288, to get

694 = 288 x 2 + 118

Step 2: Since the reminder 288 ≠ 0, we apply division lemma to 118 and 288, to get

288 = 118 x 2 + 52

Step 3: We consider the new divisor 118 and the new remainder 52, and apply the division lemma to get

118 = 52 x 2 + 14

We consider the new divisor 52 and the new remainder 14,and apply the division lemma to get

52 = 14 x 3 + 10

We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get

14 = 10 x 1 + 4

We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get

10 = 4 x 2 + 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 694 and 288 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(52,14) = HCF(118,52) = HCF(288,118) = HCF(694,288) .

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

Step 1: Since 138 > 2, we apply the division lemma to 138 and 2, to get

138 = 2 x 69 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 138 is 2

Notice that 2 = HCF(138,2) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 694, 288, 138 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 694, 288, 138?

Answer: HCF of 694, 288, 138 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 694, 288, 138 using Euclid's Algorithm?

Answer: For arbitrary numbers 694, 288, 138 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.