Highest Common Factor of 429, 689, 99 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, 689, 99 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 429, 689, 99 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 429, 689, 99 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, 689, 99 is 1.
HCF(429, 689, 99) = 1
HCF of 429, 689, 99 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, 689, 99 is 1.
Highest Common Factor of 429,689,99 is 1
Step 1: Since 689 > 429, we apply the division lemma to 689 and 429, to get
689 = 429 x 1 + 260
Step 2: Since the reminder 429 ≠ 0, we apply division lemma to 260 and 429, to get
429 = 260 x 1 + 169
Step 3: We consider the new divisor 260 and the new remainder 169, and apply the division lemma to get
260 = 169 x 1 + 91
We consider the new divisor 169 and the new remainder 91,and apply the division lemma to get
169 = 91 x 1 + 78
We consider the new divisor 91 and the new remainder 78,and apply the division lemma to get
91 = 78 x 1 + 13
We consider the new divisor 78 and the new remainder 13,and apply the division lemma to get
78 = 13 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 429 and 689 is 13
Notice that 13 = HCF(78,13) = HCF(91,78) = HCF(169,91) = HCF(260,169) = HCF(429,260) = HCF(689,429) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 99 > 13, we apply the division lemma to 99 and 13, to get
99 = 13 x 7 + 8
Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 8 and 13, to get
13 = 8 x 1 + 5
Step 3: We consider the new divisor 8 and the new remainder 5, and apply the division lemma to get
8 = 5 x 1 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 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 13 and 99 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(99,13) .
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Frequently Asked Questions on HCF of 429, 689, 99 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, 689, 99?
Answer: HCF of 429, 689, 99 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 429, 689, 99 using Euclid's Algorithm?
Answer: For arbitrary numbers 429, 689, 99 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
