Highest Common Factor of 690, 340 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 690, 340 i.e. 10 the largest integer that leaves a remainder zero for all numbers.

HCF of 690, 340 is 10 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 690, 340 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 690, 340 is 10.

HCF(690, 340) = 10

HCF of 690, 340 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 690, 340 is 10.

Highest Common Factor of 690,340 using Euclid's algorithm

Highest Common Factor of 690,340 is 10

Step 1: Since 690 > 340, we apply the division lemma to 690 and 340, to get

690 = 340 x 2 + 10

Step 2: Since the reminder 340 ≠ 0, we apply division lemma to 10 and 340, to get

340 = 10 x 34 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 690 and 340 is 10

Notice that 10 = HCF(340,10) = HCF(690,340) .

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Frequently Asked Questions on HCF of 690, 340 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 690, 340?

Answer: HCF of 690, 340 is 10 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 690, 340 using Euclid's Algorithm?

Answer: For arbitrary numbers 690, 340 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.