Highest Common Factor of 405, 964, 692 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, 964, 692 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 405, 964, 692 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, 964, 692 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, 964, 692 is 1.
HCF(405, 964, 692) = 1
HCF of 405, 964, 692 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, 964, 692 is 1.
Highest Common Factor of 405,964,692 is 1
Step 1: Since 964 > 405, we apply the division lemma to 964 and 405, to get
964 = 405 x 2 + 154
Step 2: Since the reminder 405 ≠ 0, we apply division lemma to 154 and 405, to get
405 = 154 x 2 + 97
Step 3: We consider the new divisor 154 and the new remainder 97, and apply the division lemma to get
154 = 97 x 1 + 57
We consider the new divisor 97 and the new remainder 57,and apply the division lemma to get
97 = 57 x 1 + 40
We consider the new divisor 57 and the new remainder 40,and apply the division lemma to get
57 = 40 x 1 + 17
We consider the new divisor 40 and the new remainder 17,and apply the division lemma to get
40 = 17 x 2 + 6
We consider the new divisor 17 and the new remainder 6,and apply the division lemma to get
17 = 6 x 2 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 405 and 964 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(17,6) = HCF(40,17) = HCF(57,40) = HCF(97,57) = HCF(154,97) = HCF(405,154) = HCF(964,405) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 692 > 1, we apply the division lemma to 692 and 1, to get
692 = 1 x 692 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 692 is 1
Notice that 1 = HCF(692,1) .
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Frequently Asked Questions on HCF of 405, 964, 692 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, 964, 692?
Answer: HCF of 405, 964, 692 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 405, 964, 692 using Euclid's Algorithm?
Answer: For arbitrary numbers 405, 964, 692 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.