Highest Common Factor of 800, 165, 42, 404 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 800, 165, 42, 404 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 800, 165, 42, 404 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 800, 165, 42, 404 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 800, 165, 42, 404 is 1.
HCF(800, 165, 42, 404) = 1
HCF of 800, 165, 42, 404 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 800, 165, 42, 404 is 1.
Highest Common Factor of 800,165,42,404 is 1
Step 1: Since 800 > 165, we apply the division lemma to 800 and 165, to get
800 = 165 x 4 + 140
Step 2: Since the reminder 165 ≠ 0, we apply division lemma to 140 and 165, to get
165 = 140 x 1 + 25
Step 3: We consider the new divisor 140 and the new remainder 25, and apply the division lemma to get
140 = 25 x 5 + 15
We consider the new divisor 25 and the new remainder 15,and apply the division lemma to get
25 = 15 x 1 + 10
We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get
15 = 10 x 1 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 800 and 165 is 5
Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(25,15) = HCF(140,25) = HCF(165,140) = HCF(800,165) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 42 > 5, we apply the division lemma to 42 and 5, to get
42 = 5 x 8 + 2
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 2 and 5, to get
5 = 2 x 2 + 1
Step 3: 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 5 and 42 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(42,5) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 404 > 1, we apply the division lemma to 404 and 1, to get
404 = 1 x 404 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 404 is 1
Notice that 1 = HCF(404,1) .
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Frequently Asked Questions on HCF of 800, 165, 42, 404 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 800, 165, 42, 404?
Answer: HCF of 800, 165, 42, 404 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 800, 165, 42, 404 using Euclid's Algorithm?
Answer: For arbitrary numbers 800, 165, 42, 404 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.