Highest Common Factor of 690, 810 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, 810 i.e. 30 the largest integer that leaves a remainder zero for all numbers.
HCF of 690, 810 is 30 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, 810 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, 810 is 30.
HCF(690, 810) = 30
HCF of 690, 810 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 690, 810 is 30.
Highest Common Factor of 690,810 is 30
Step 1: Since 810 > 690, we apply the division lemma to 810 and 690, to get
810 = 690 x 1 + 120
Step 2: Since the reminder 690 ≠ 0, we apply division lemma to 120 and 690, to get
690 = 120 x 5 + 90
Step 3: We consider the new divisor 120 and the new remainder 90, and apply the division lemma to get
120 = 90 x 1 + 30
We consider the new divisor 90 and the new remainder 30, and apply the division lemma to get
90 = 30 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 30, the HCF of 690 and 810 is 30
Notice that 30 = HCF(90,30) = HCF(120,90) = HCF(690,120) = HCF(810,690) .
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Frequently Asked Questions on HCF of 690, 810 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, 810?
Answer: HCF of 690, 810 is 30 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 690, 810 using Euclid's Algorithm?
Answer: For arbitrary numbers 690, 810 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.