Highest Common Factor of 684, 954, 43, 166 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 684, 954, 43, 166 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 684, 954, 43, 166 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 684, 954, 43, 166 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 684, 954, 43, 166 is 1.

HCF(684, 954, 43, 166) = 1

HCF of 684, 954, 43, 166 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 684, 954, 43, 166 is 1.

Highest Common Factor of 684,954,43,166 using Euclid's algorithm

Highest Common Factor of 684,954,43,166 is 1

Step 1: Since 954 > 684, we apply the division lemma to 954 and 684, to get

954 = 684 x 1 + 270

Step 2: Since the reminder 684 ≠ 0, we apply division lemma to 270 and 684, to get

684 = 270 x 2 + 144

Step 3: We consider the new divisor 270 and the new remainder 144, and apply the division lemma to get

270 = 144 x 1 + 126

We consider the new divisor 144 and the new remainder 126,and apply the division lemma to get

144 = 126 x 1 + 18

We consider the new divisor 126 and the new remainder 18,and apply the division lemma to get

126 = 18 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 684 and 954 is 18

Notice that 18 = HCF(126,18) = HCF(144,126) = HCF(270,144) = HCF(684,270) = HCF(954,684) .

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

Step 1: Since 43 > 18, we apply the division lemma to 43 and 18, to get

43 = 18 x 2 + 7

Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 7 and 18, to get

18 = 7 x 2 + 4

Step 3: We consider the new divisor 7 and the new remainder 4, and apply the division lemma to get

7 = 4 x 1 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 18 and 43 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(18,7) = HCF(43,18) .

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

Step 1: Since 166 > 1, we apply the division lemma to 166 and 1, to get

166 = 1 x 166 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 166 is 1

Notice that 1 = HCF(166,1) .

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Frequently Asked Questions on HCF of 684, 954, 43, 166 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 684, 954, 43, 166?

Answer: HCF of 684, 954, 43, 166 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 684, 954, 43, 166 using Euclid's Algorithm?

Answer: For arbitrary numbers 684, 954, 43, 166 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.