Highest Common Factor of 168, 538, 69 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 168, 538, 69 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 168, 538, 69 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 168, 538, 69 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 168, 538, 69 is 1.
HCF(168, 538, 69) = 1
HCF of 168, 538, 69 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 168, 538, 69 is 1.
Highest Common Factor of 168,538,69 is 1
Step 1: Since 538 > 168, we apply the division lemma to 538 and 168, to get
538 = 168 x 3 + 34
Step 2: Since the reminder 168 ≠ 0, we apply division lemma to 34 and 168, to get
168 = 34 x 4 + 32
Step 3: We consider the new divisor 34 and the new remainder 32, and apply the division lemma to get
34 = 32 x 1 + 2
We consider the new divisor 32 and the new remainder 2, and apply the division lemma to get
32 = 2 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 168 and 538 is 2
Notice that 2 = HCF(32,2) = HCF(34,32) = HCF(168,34) = HCF(538,168) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 69 > 2, we apply the division lemma to 69 and 2, to get
69 = 2 x 34 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 69 is 1
Notice that 1 = HCF(2,1) = HCF(69,2) .
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Frequently Asked Questions on HCF of 168, 538, 69 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 168, 538, 69?
Answer: HCF of 168, 538, 69 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 168, 538, 69 using Euclid's Algorithm?
Answer: For arbitrary numbers 168, 538, 69 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.