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, 207, 934 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 690, 207, 934 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 690, 207, 934 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, 207, 934 is 1.
HCF(690, 207, 934) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 690, 207, 934 is 1.
Step 1: Since 690 > 207, we apply the division lemma to 690 and 207, to get
690 = 207 x 3 + 69
Step 2: Since the reminder 207 ≠ 0, we apply division lemma to 69 and 207, to get
207 = 69 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 69, the HCF of 690 and 207 is 69
Notice that 69 = HCF(207,69) = HCF(690,207) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 934 > 69, we apply the division lemma to 934 and 69, to get
934 = 69 x 13 + 37
Step 2: Since the reminder 69 ≠ 0, we apply division lemma to 37 and 69, to get
69 = 37 x 1 + 32
Step 3: We consider the new divisor 37 and the new remainder 32, and apply the division lemma to get
37 = 32 x 1 + 5
We consider the new divisor 32 and the new remainder 5,and apply the division lemma to get
32 = 5 x 6 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 69 and 934 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(32,5) = HCF(37,32) = HCF(69,37) = HCF(934,69) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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, 207, 934?
Answer: HCF of 690, 207, 934 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 690, 207, 934 using Euclid's Algorithm?
Answer: For arbitrary numbers 690, 207, 934 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.