Highest Common Factor of 429, 660, 735 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, 660, 735 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 429, 660, 735 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, 660, 735 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, 660, 735 is 3.
HCF(429, 660, 735) = 3
HCF of 429, 660, 735 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, 660, 735 is 3.
Highest Common Factor of 429,660,735 is 3
Step 1: Since 660 > 429, we apply the division lemma to 660 and 429, to get
660 = 429 x 1 + 231
Step 2: Since the reminder 429 ≠ 0, we apply division lemma to 231 and 429, to get
429 = 231 x 1 + 198
Step 3: We consider the new divisor 231 and the new remainder 198, and apply the division lemma to get
231 = 198 x 1 + 33
We consider the new divisor 198 and the new remainder 33, and apply the division lemma to get
198 = 33 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 33, the HCF of 429 and 660 is 33
Notice that 33 = HCF(198,33) = HCF(231,198) = HCF(429,231) = HCF(660,429) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 735 > 33, we apply the division lemma to 735 and 33, to get
735 = 33 x 22 + 9
Step 2: Since the reminder 33 ≠ 0, we apply division lemma to 9 and 33, to get
33 = 9 x 3 + 6
Step 3: We consider the new divisor 9 and the new remainder 6, and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3, and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 33 and 735 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(33,9) = HCF(735,33) .
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Frequently Asked Questions on HCF of 429, 660, 735 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, 660, 735?
Answer: HCF of 429, 660, 735 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 429, 660, 735 using Euclid's Algorithm?
Answer: For arbitrary numbers 429, 660, 735 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.