Highest Common Factor of 800, 30, 134, 584 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, 30, 134, 584 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 800, 30, 134, 584 is 2 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, 30, 134, 584 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, 30, 134, 584 is 2.
HCF(800, 30, 134, 584) = 2
HCF of 800, 30, 134, 584 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, 30, 134, 584 is 2.
Highest Common Factor of 800,30,134,584 is 2
Step 1: Since 800 > 30, we apply the division lemma to 800 and 30, to get
800 = 30 x 26 + 20
Step 2: Since the reminder 30 ≠ 0, we apply division lemma to 20 and 30, to get
30 = 20 x 1 + 10
Step 3: We consider the new divisor 20 and the new remainder 10, and apply the division lemma to get
20 = 10 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 800 and 30 is 10
Notice that 10 = HCF(20,10) = HCF(30,20) = HCF(800,30) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 134 > 10, we apply the division lemma to 134 and 10, to get
134 = 10 x 13 + 4
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 4 and 10, to get
10 = 4 x 2 + 2
Step 3: We consider the new divisor 4 and the new remainder 2, and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 10 and 134 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(134,10) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 584 > 2, we apply the division lemma to 584 and 2, to get
584 = 2 x 292 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 584 is 2
Notice that 2 = HCF(584,2) .
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Frequently Asked Questions on HCF of 800, 30, 134, 584 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, 30, 134, 584?
Answer: HCF of 800, 30, 134, 584 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 800, 30, 134, 584 using Euclid's Algorithm?
Answer: For arbitrary numbers 800, 30, 134, 584 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
