Highest Common Factor of 400, 693, 645 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 400, 693, 645 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 400, 693, 645 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 400, 693, 645 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 400, 693, 645 is 1.
HCF(400, 693, 645) = 1
HCF of 400, 693, 645 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 400, 693, 645 is 1.
Highest Common Factor of 400,693,645 is 1
Step 1: Since 693 > 400, we apply the division lemma to 693 and 400, to get
693 = 400 x 1 + 293
Step 2: Since the reminder 400 ≠ 0, we apply division lemma to 293 and 400, to get
400 = 293 x 1 + 107
Step 3: We consider the new divisor 293 and the new remainder 107, and apply the division lemma to get
293 = 107 x 2 + 79
We consider the new divisor 107 and the new remainder 79,and apply the division lemma to get
107 = 79 x 1 + 28
We consider the new divisor 79 and the new remainder 28,and apply the division lemma to get
79 = 28 x 2 + 23
We consider the new divisor 28 and the new remainder 23,and apply the division lemma to get
28 = 23 x 1 + 5
We consider the new divisor 23 and the new remainder 5,and apply the division lemma to get
23 = 5 x 4 + 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 400 and 693 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(23,5) = HCF(28,23) = HCF(79,28) = HCF(107,79) = HCF(293,107) = HCF(400,293) = HCF(693,400) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 645 > 1, we apply the division lemma to 645 and 1, to get
645 = 1 x 645 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 645 is 1
Notice that 1 = HCF(645,1) .
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Frequently Asked Questions on HCF of 400, 693, 645 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 400, 693, 645?
Answer: HCF of 400, 693, 645 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 400, 693, 645 using Euclid's Algorithm?
Answer: For arbitrary numbers 400, 693, 645 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.