Highest Common Factor of 690, 840, 17 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, 840, 17 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 690, 840, 17 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, 840, 17 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, 840, 17 is 1.
HCF(690, 840, 17) = 1
HCF of 690, 840, 17 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, 840, 17 is 1.
Highest Common Factor of 690,840,17 is 1
Step 1: Since 840 > 690, we apply the division lemma to 840 and 690, to get
840 = 690 x 1 + 150
Step 2: Since the reminder 690 ≠ 0, we apply division lemma to 150 and 690, to get
690 = 150 x 4 + 90
Step 3: We consider the new divisor 150 and the new remainder 90, and apply the division lemma to get
150 = 90 x 1 + 60
We consider the new divisor 90 and the new remainder 60,and apply the division lemma to get
90 = 60 x 1 + 30
We consider the new divisor 60 and the new remainder 30,and apply the division lemma to get
60 = 30 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 30, the HCF of 690 and 840 is 30
Notice that 30 = HCF(60,30) = HCF(90,60) = HCF(150,90) = HCF(690,150) = HCF(840,690) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 30 > 17, we apply the division lemma to 30 and 17, to get
30 = 17 x 1 + 13
Step 2: Since the reminder 17 ≠ 0, we apply division lemma to 13 and 17, to get
17 = 13 x 1 + 4
Step 3: We consider the new divisor 13 and the new remainder 4, and apply the division lemma to get
13 = 4 x 3 + 1
We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 30 and 17 is 1
Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(17,13) = HCF(30,17) .
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Frequently Asked Questions on HCF of 690, 840, 17 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, 840, 17?
Answer: HCF of 690, 840, 17 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 690, 840, 17 using Euclid's Algorithm?
Answer: For arbitrary numbers 690, 840, 17 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.