Highest Common Factor of 222, 588, 34 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 222, 588, 34 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 222, 588, 34 is 2 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 222, 588, 34 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 222, 588, 34 is 2.
HCF(222, 588, 34) = 2
HCF of 222, 588, 34 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 222, 588, 34 is 2.
Highest Common Factor of 222,588,34 is 2
Step 1: Since 588 > 222, we apply the division lemma to 588 and 222, to get
588 = 222 x 2 + 144
Step 2: Since the reminder 222 ≠ 0, we apply division lemma to 144 and 222, to get
222 = 144 x 1 + 78
Step 3: We consider the new divisor 144 and the new remainder 78, and apply the division lemma to get
144 = 78 x 1 + 66
We consider the new divisor 78 and the new remainder 66,and apply the division lemma to get
78 = 66 x 1 + 12
We consider the new divisor 66 and the new remainder 12,and apply the division lemma to get
66 = 12 x 5 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 222 and 588 is 6
Notice that 6 = HCF(12,6) = HCF(66,12) = HCF(78,66) = HCF(144,78) = HCF(222,144) = HCF(588,222) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 34 > 6, we apply the division lemma to 34 and 6, to get
34 = 6 x 5 + 4
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 4 and 6, to get
6 = 4 x 1 + 2
Step 3: We consider the new divisor 4 and the new remainder 2, and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6 and 34 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(34,6) .
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Frequently Asked Questions on HCF of 222, 588, 34 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 222, 588, 34?
Answer: HCF of 222, 588, 34 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 222, 588, 34 using Euclid's Algorithm?
Answer: For arbitrary numbers 222, 588, 34 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.