Highest Common Factor of 405, 662, 35 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 405, 662, 35 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 405, 662, 35 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 405, 662, 35 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 405, 662, 35 is 1.
HCF(405, 662, 35) = 1
HCF of 405, 662, 35 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 405, 662, 35 is 1.
Highest Common Factor of 405,662,35 is 1
Step 1: Since 662 > 405, we apply the division lemma to 662 and 405, to get
662 = 405 x 1 + 257
Step 2: Since the reminder 405 ≠ 0, we apply division lemma to 257 and 405, to get
405 = 257 x 1 + 148
Step 3: We consider the new divisor 257 and the new remainder 148, and apply the division lemma to get
257 = 148 x 1 + 109
We consider the new divisor 148 and the new remainder 109,and apply the division lemma to get
148 = 109 x 1 + 39
We consider the new divisor 109 and the new remainder 39,and apply the division lemma to get
109 = 39 x 2 + 31
We consider the new divisor 39 and the new remainder 31,and apply the division lemma to get
39 = 31 x 1 + 8
We consider the new divisor 31 and the new remainder 8,and apply the division lemma to get
31 = 8 x 3 + 7
We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get
8 = 7 x 1 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 405 and 662 is 1
Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(31,8) = HCF(39,31) = HCF(109,39) = HCF(148,109) = HCF(257,148) = HCF(405,257) = HCF(662,405) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 35 > 1, we apply the division lemma to 35 and 1, to get
35 = 1 x 35 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 35 is 1
Notice that 1 = HCF(35,1) .
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Frequently Asked Questions on HCF of 405, 662, 35 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 405, 662, 35?
Answer: HCF of 405, 662, 35 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 405, 662, 35 using Euclid's Algorithm?
Answer: For arbitrary numbers 405, 662, 35 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.