Highest Common Factor of 426, 688, 84 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 426, 688, 84 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 426, 688, 84 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 426, 688, 84 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 426, 688, 84 is 2.

HCF(426, 688, 84) = 2

HCF of 426, 688, 84 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 426, 688, 84 is 2.

Highest Common Factor of 426,688,84 using Euclid's algorithm

Highest Common Factor of 426,688,84 is 2

Step 1: Since 688 > 426, we apply the division lemma to 688 and 426, to get

688 = 426 x 1 + 262

Step 2: Since the reminder 426 ≠ 0, we apply division lemma to 262 and 426, to get

426 = 262 x 1 + 164

Step 3: We consider the new divisor 262 and the new remainder 164, and apply the division lemma to get

262 = 164 x 1 + 98

We consider the new divisor 164 and the new remainder 98,and apply the division lemma to get

164 = 98 x 1 + 66

We consider the new divisor 98 and the new remainder 66,and apply the division lemma to get

98 = 66 x 1 + 32

We consider the new divisor 66 and the new remainder 32,and apply the division lemma to get

66 = 32 x 2 + 2

We consider the new divisor 32 and the new remainder 2,and apply the division lemma to get

32 = 2 x 16 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 426 and 688 is 2

Notice that 2 = HCF(32,2) = HCF(66,32) = HCF(98,66) = HCF(164,98) = HCF(262,164) = HCF(426,262) = HCF(688,426) .

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

Step 1: Since 84 > 2, we apply the division lemma to 84 and 2, to get

84 = 2 x 42 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 84 is 2

Notice that 2 = HCF(84,2) .

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Frequently Asked Questions on HCF of 426, 688, 84 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 426, 688, 84?

Answer: HCF of 426, 688, 84 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 426, 688, 84 using Euclid's Algorithm?

Answer: For arbitrary numbers 426, 688, 84 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.