Highest Common Factor of 429, 693 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, 693 i.e. 33 the largest integer that leaves a remainder zero for all numbers.
HCF of 429, 693 is 33 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, 693 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, 693 is 33.
HCF(429, 693) = 33
HCF of 429, 693 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, 693 is 33.
Highest Common Factor of 429,693 is 33
Step 1: Since 693 > 429, we apply the division lemma to 693 and 429, to get
693 = 429 x 1 + 264
Step 2: Since the reminder 429 ≠ 0, we apply division lemma to 264 and 429, to get
429 = 264 x 1 + 165
Step 3: We consider the new divisor 264 and the new remainder 165, and apply the division lemma to get
264 = 165 x 1 + 99
We consider the new divisor 165 and the new remainder 99,and apply the division lemma to get
165 = 99 x 1 + 66
We consider the new divisor 99 and the new remainder 66,and apply the division lemma to get
99 = 66 x 1 + 33
We consider the new divisor 66 and the new remainder 33,and apply the division lemma to get
66 = 33 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 33, the HCF of 429 and 693 is 33
Notice that 33 = HCF(66,33) = HCF(99,66) = HCF(165,99) = HCF(264,165) = HCF(429,264) = HCF(693,429) .
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Frequently Asked Questions on HCF of 429, 693 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, 693?
Answer: HCF of 429, 693 is 33 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 429, 693 using Euclid's Algorithm?
Answer: For arbitrary numbers 429, 693 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.