Highest Common Factor of 429, 585, 690 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 429, 585, 690 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 429, 585, 690 is 3 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 429, 585, 690 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 429, 585, 690 is 3.
HCF(429, 585, 690) = 3
HCF of 429, 585, 690 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 429, 585, 690 is 3.
Highest Common Factor of 429,585,690 is 3
Step 1: Since 585 > 429, we apply the division lemma to 585 and 429, to get
585 = 429 x 1 + 156
Step 2: Since the reminder 429 ≠ 0, we apply division lemma to 156 and 429, to get
429 = 156 x 2 + 117
Step 3: We consider the new divisor 156 and the new remainder 117, and apply the division lemma to get
156 = 117 x 1 + 39
We consider the new divisor 117 and the new remainder 39, and apply the division lemma to get
117 = 39 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 39, the HCF of 429 and 585 is 39
Notice that 39 = HCF(117,39) = HCF(156,117) = HCF(429,156) = HCF(585,429) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 690 > 39, we apply the division lemma to 690 and 39, to get
690 = 39 x 17 + 27
Step 2: Since the reminder 39 ≠ 0, we apply division lemma to 27 and 39, to get
39 = 27 x 1 + 12
Step 3: We consider the new divisor 27 and the new remainder 12, and apply the division lemma to get
27 = 12 x 2 + 3
We consider the new divisor 12 and the new remainder 3, and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 39 and 690 is 3
Notice that 3 = HCF(12,3) = HCF(27,12) = HCF(39,27) = HCF(690,39) .
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Frequently Asked Questions on HCF of 429, 585, 690 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 429, 585, 690?
Answer: HCF of 429, 585, 690 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 429, 585, 690 using Euclid's Algorithm?
Answer: For arbitrary numbers 429, 585, 690 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.