Highest Common Factor of 83, 154, 210 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 83, 154, 210 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 83, 154, 210 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 83, 154, 210 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 83, 154, 210 is 1.
HCF(83, 154, 210) = 1
HCF of 83, 154, 210 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 83, 154, 210 is 1.
Highest Common Factor of 83,154,210 is 1
Step 1: Since 154 > 83, we apply the division lemma to 154 and 83, to get
154 = 83 x 1 + 71
Step 2: Since the reminder 83 ≠ 0, we apply division lemma to 71 and 83, to get
83 = 71 x 1 + 12
Step 3: We consider the new divisor 71 and the new remainder 12, and apply the division lemma to get
71 = 12 x 5 + 11
We consider the new divisor 12 and the new remainder 11,and apply the division lemma to get
12 = 11 x 1 + 1
We consider the new divisor 11 and the new remainder 1,and apply the division lemma to get
11 = 1 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 83 and 154 is 1
Notice that 1 = HCF(11,1) = HCF(12,11) = HCF(71,12) = HCF(83,71) = HCF(154,83) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 210 > 1, we apply the division lemma to 210 and 1, to get
210 = 1 x 210 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 210 is 1
Notice that 1 = HCF(210,1) .
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Frequently Asked Questions on HCF of 83, 154, 210 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 83, 154, 210?
Answer: HCF of 83, 154, 210 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 83, 154, 210 using Euclid's Algorithm?
Answer: For arbitrary numbers 83, 154, 210 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.