Highest Common Factor of 608, 209, 55 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 608, 209, 55 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 608, 209, 55 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 608, 209, 55 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 608, 209, 55 is 1.
HCF(608, 209, 55) = 1
HCF of 608, 209, 55 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 608, 209, 55 is 1.
Highest Common Factor of 608,209,55 is 1
Step 1: Since 608 > 209, we apply the division lemma to 608 and 209, to get
608 = 209 x 2 + 190
Step 2: Since the reminder 209 ≠ 0, we apply division lemma to 190 and 209, to get
209 = 190 x 1 + 19
Step 3: We consider the new divisor 190 and the new remainder 19, and apply the division lemma to get
190 = 19 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 19, the HCF of 608 and 209 is 19
Notice that 19 = HCF(190,19) = HCF(209,190) = HCF(608,209) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 55 > 19, we apply the division lemma to 55 and 19, to get
55 = 19 x 2 + 17
Step 2: Since the reminder 19 ≠ 0, we apply division lemma to 17 and 19, to get
19 = 17 x 1 + 2
Step 3: We consider the new divisor 17 and the new remainder 2, and apply the division lemma to get
17 = 2 x 8 + 1
We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 19 and 55 is 1
Notice that 1 = HCF(2,1) = HCF(17,2) = HCF(19,17) = HCF(55,19) .
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Frequently Asked Questions on HCF of 608, 209, 55 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 608, 209, 55?
Answer: HCF of 608, 209, 55 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 608, 209, 55 using Euclid's Algorithm?
Answer: For arbitrary numbers 608, 209, 55 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.