Highest Common Factor of 854, 745, 168 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, 745, 168 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 854, 745, 168 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, 745, 168 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, 745, 168 is 1.
HCF(854, 745, 168) = 1
HCF of 854, 745, 168 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, 745, 168 is 1.
Highest Common Factor of 854,745,168 is 1
Step 1: Since 854 > 745, we apply the division lemma to 854 and 745, to get
854 = 745 x 1 + 109
Step 2: Since the reminder 745 ≠ 0, we apply division lemma to 109 and 745, to get
745 = 109 x 6 + 91
Step 3: We consider the new divisor 109 and the new remainder 91, and apply the division lemma to get
109 = 91 x 1 + 18
We consider the new divisor 91 and the new remainder 18,and apply the division lemma to get
91 = 18 x 5 + 1
We consider the new divisor 18 and the new remainder 1,and apply the division lemma to get
18 = 1 x 18 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 854 and 745 is 1
Notice that 1 = HCF(18,1) = HCF(91,18) = HCF(109,91) = HCF(745,109) = HCF(854,745) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 168 > 1, we apply the division lemma to 168 and 1, to get
168 = 1 x 168 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 168 is 1
Notice that 1 = HCF(168,1) .
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Frequently Asked Questions on HCF of 854, 745, 168 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, 745, 168?
Answer: HCF of 854, 745, 168 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 854, 745, 168 using Euclid's Algorithm?
Answer: For arbitrary numbers 854, 745, 168 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.