Highest Common Factor of 434, 600, 690 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 434, 600, 690 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 434, 600, 690 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 434, 600, 690 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 434, 600, 690 is 2.

HCF(434, 600, 690) = 2

HCF of 434, 600, 690 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 434, 600, 690 is 2.

Highest Common Factor of 434,600,690 using Euclid's algorithm

Highest Common Factor of 434,600,690 is 2

Step 1: Since 600 > 434, we apply the division lemma to 600 and 434, to get

600 = 434 x 1 + 166

Step 2: Since the reminder 434 ≠ 0, we apply division lemma to 166 and 434, to get

434 = 166 x 2 + 102

Step 3: We consider the new divisor 166 and the new remainder 102, and apply the division lemma to get

166 = 102 x 1 + 64

We consider the new divisor 102 and the new remainder 64,and apply the division lemma to get

102 = 64 x 1 + 38

We consider the new divisor 64 and the new remainder 38,and apply the division lemma to get

64 = 38 x 1 + 26

We consider the new divisor 38 and the new remainder 26,and apply the division lemma to get

38 = 26 x 1 + 12

We consider the new divisor 26 and the new remainder 12,and apply the division lemma to get

26 = 12 x 2 + 2

We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get

12 = 2 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 434 and 600 is 2

Notice that 2 = HCF(12,2) = HCF(26,12) = HCF(38,26) = HCF(64,38) = HCF(102,64) = HCF(166,102) = HCF(434,166) = HCF(600,434) .

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

Step 1: Since 690 > 2, we apply the division lemma to 690 and 2, to get

690 = 2 x 345 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 690 is 2

Notice that 2 = HCF(690,2) .

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Frequently Asked Questions on HCF of 434, 600, 690 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 434, 600, 690?

Answer: HCF of 434, 600, 690 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 434, 600, 690 using Euclid's Algorithm?

Answer: For arbitrary numbers 434, 600, 690 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.