Highest Common Factor of 854, 385, 120 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, 385, 120 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 854, 385, 120 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, 385, 120 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, 385, 120 is 1.
HCF(854, 385, 120) = 1
HCF of 854, 385, 120 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, 385, 120 is 1.
Highest Common Factor of 854,385,120 is 1
Step 1: Since 854 > 385, we apply the division lemma to 854 and 385, to get
854 = 385 x 2 + 84
Step 2: Since the reminder 385 ≠ 0, we apply division lemma to 84 and 385, to get
385 = 84 x 4 + 49
Step 3: We consider the new divisor 84 and the new remainder 49, and apply the division lemma to get
84 = 49 x 1 + 35
We consider the new divisor 49 and the new remainder 35,and apply the division lemma to get
49 = 35 x 1 + 14
We consider the new divisor 35 and the new remainder 14,and apply the division lemma to get
35 = 14 x 2 + 7
We consider the new divisor 14 and the new remainder 7,and apply the division lemma to get
14 = 7 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 854 and 385 is 7
Notice that 7 = HCF(14,7) = HCF(35,14) = HCF(49,35) = HCF(84,49) = HCF(385,84) = HCF(854,385) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 120 > 7, we apply the division lemma to 120 and 7, to get
120 = 7 x 17 + 1
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 1 and 7, to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7 and 120 is 1
Notice that 1 = HCF(7,1) = HCF(120,7) .
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Frequently Asked Questions on HCF of 854, 385, 120 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, 385, 120?
Answer: HCF of 854, 385, 120 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 854, 385, 120 using Euclid's Algorithm?
Answer: For arbitrary numbers 854, 385, 120 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.