Highest Common Factor of 854, 224, 873 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 854, 224, 873 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 854, 224, 873 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 854, 224, 873 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 854, 224, 873 is 1.
HCF(854, 224, 873) = 1
HCF of 854, 224, 873 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 854, 224, 873 is 1.
Highest Common Factor of 854,224,873 is 1
Step 1: Since 854 > 224, we apply the division lemma to 854 and 224, to get
854 = 224 x 3 + 182
Step 2: Since the reminder 224 ≠ 0, we apply division lemma to 182 and 224, to get
224 = 182 x 1 + 42
Step 3: We consider the new divisor 182 and the new remainder 42, and apply the division lemma to get
182 = 42 x 4 + 14
We consider the new divisor 42 and the new remainder 14, and apply the division lemma to get
42 = 14 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 854 and 224 is 14
Notice that 14 = HCF(42,14) = HCF(182,42) = HCF(224,182) = HCF(854,224) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 873 > 14, we apply the division lemma to 873 and 14, to get
873 = 14 x 62 + 5
Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 5 and 14, to get
14 = 5 x 2 + 4
Step 3: We consider the new divisor 5 and the new remainder 4, and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 14 and 873 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(873,14) .
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Frequently Asked Questions on HCF of 854, 224, 873 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 854, 224, 873?
Answer: HCF of 854, 224, 873 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 854, 224, 873 using Euclid's Algorithm?
Answer: For arbitrary numbers 854, 224, 873 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.