Highest Common Factor of 222, 578 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, 578 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 222, 578 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, 578 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, 578 is 2.
HCF(222, 578) = 2
HCF of 222, 578 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, 578 is 2.
Highest Common Factor of 222,578 is 2
Step 1: Since 578 > 222, we apply the division lemma to 578 and 222, to get
578 = 222 x 2 + 134
Step 2: Since the reminder 222 ≠ 0, we apply division lemma to 134 and 222, to get
222 = 134 x 1 + 88
Step 3: We consider the new divisor 134 and the new remainder 88, and apply the division lemma to get
134 = 88 x 1 + 46
We consider the new divisor 88 and the new remainder 46,and apply the division lemma to get
88 = 46 x 1 + 42
We consider the new divisor 46 and the new remainder 42,and apply the division lemma to get
46 = 42 x 1 + 4
We consider the new divisor 42 and the new remainder 4,and apply the division lemma to get
42 = 4 x 10 + 2
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 222 and 578 is 2
Notice that 2 = HCF(4,2) = HCF(42,4) = HCF(46,42) = HCF(88,46) = HCF(134,88) = HCF(222,134) = HCF(578,222) .
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Frequently Asked Questions on HCF of 222, 578 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, 578?
Answer: HCF of 222, 578 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 222, 578 using Euclid's Algorithm?
Answer: For arbitrary numbers 222, 578 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.