Highest Common Factor of 6216, 8578 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 6216, 8578 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 6216, 8578 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 6216, 8578 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 6216, 8578 is 2.
HCF(6216, 8578) = 2
HCF of 6216, 8578 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6216, 8578 is 2.
Highest Common Factor of 6216,8578 is 2
Step 1: Since 8578 > 6216, we apply the division lemma to 8578 and 6216, to get
8578 = 6216 x 1 + 2362
Step 2: Since the reminder 6216 ≠ 0, we apply division lemma to 2362 and 6216, to get
6216 = 2362 x 2 + 1492
Step 3: We consider the new divisor 2362 and the new remainder 1492, and apply the division lemma to get
2362 = 1492 x 1 + 870
We consider the new divisor 1492 and the new remainder 870,and apply the division lemma to get
1492 = 870 x 1 + 622
We consider the new divisor 870 and the new remainder 622,and apply the division lemma to get
870 = 622 x 1 + 248
We consider the new divisor 622 and the new remainder 248,and apply the division lemma to get
622 = 248 x 2 + 126
We consider the new divisor 248 and the new remainder 126,and apply the division lemma to get
248 = 126 x 1 + 122
We consider the new divisor 126 and the new remainder 122,and apply the division lemma to get
126 = 122 x 1 + 4
We consider the new divisor 122 and the new remainder 4,and apply the division lemma to get
122 = 4 x 30 + 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 6216 and 8578 is 2
Notice that 2 = HCF(4,2) = HCF(122,4) = HCF(126,122) = HCF(248,126) = HCF(622,248) = HCF(870,622) = HCF(1492,870) = HCF(2362,1492) = HCF(6216,2362) = HCF(8578,6216) .
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Frequently Asked Questions on HCF of 6216, 8578 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 6216, 8578?
Answer: HCF of 6216, 8578 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6216, 8578 using Euclid's Algorithm?
Answer: For arbitrary numbers 6216, 8578 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.