Highest Common Factor of 690, 828, 367 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, 828, 367 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 690, 828, 367 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, 828, 367 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, 828, 367 is 1.
HCF(690, 828, 367) = 1
HCF of 690, 828, 367 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, 828, 367 is 1.
Highest Common Factor of 690,828,367 is 1
Step 1: Since 828 > 690, we apply the division lemma to 828 and 690, to get
828 = 690 x 1 + 138
Step 2: Since the reminder 690 ≠ 0, we apply division lemma to 138 and 690, to get
690 = 138 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 138, the HCF of 690 and 828 is 138
Notice that 138 = HCF(690,138) = HCF(828,690) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 367 > 138, we apply the division lemma to 367 and 138, to get
367 = 138 x 2 + 91
Step 2: Since the reminder 138 ≠ 0, we apply division lemma to 91 and 138, to get
138 = 91 x 1 + 47
Step 3: We consider the new divisor 91 and the new remainder 47, and apply the division lemma to get
91 = 47 x 1 + 44
We consider the new divisor 47 and the new remainder 44,and apply the division lemma to get
47 = 44 x 1 + 3
We consider the new divisor 44 and the new remainder 3,and apply the division lemma to get
44 = 3 x 14 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 138 and 367 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(44,3) = HCF(47,44) = HCF(91,47) = HCF(138,91) = HCF(367,138) .
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Frequently Asked Questions on HCF of 690, 828, 367 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, 828, 367?
Answer: HCF of 690, 828, 367 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 690, 828, 367 using Euclid's Algorithm?
Answer: For arbitrary numbers 690, 828, 367 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
