Highest Common Factor of 668, 610, 102, 63 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 668, 610, 102, 63 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 668, 610, 102, 63 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 668, 610, 102, 63 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 668, 610, 102, 63 is 1.
HCF(668, 610, 102, 63) = 1
HCF of 668, 610, 102, 63 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 668, 610, 102, 63 is 1.
Highest Common Factor of 668,610,102,63 is 1
Step 1: Since 668 > 610, we apply the division lemma to 668 and 610, to get
668 = 610 x 1 + 58
Step 2: Since the reminder 610 ≠ 0, we apply division lemma to 58 and 610, to get
610 = 58 x 10 + 30
Step 3: We consider the new divisor 58 and the new remainder 30, and apply the division lemma to get
58 = 30 x 1 + 28
We consider the new divisor 30 and the new remainder 28,and apply the division lemma to get
30 = 28 x 1 + 2
We consider the new divisor 28 and the new remainder 2,and apply the division lemma to get
28 = 2 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 668 and 610 is 2
Notice that 2 = HCF(28,2) = HCF(30,28) = HCF(58,30) = HCF(610,58) = HCF(668,610) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 102 > 2, we apply the division lemma to 102 and 2, to get
102 = 2 x 51 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 102 is 2
Notice that 2 = HCF(102,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 63 > 2, we apply the division lemma to 63 and 2, to get
63 = 2 x 31 + 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 63 is 1
Notice that 1 = HCF(2,1) = HCF(63,2) .
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Frequently Asked Questions on HCF of 668, 610, 102, 63 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 668, 610, 102, 63?
Answer: HCF of 668, 610, 102, 63 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 668, 610, 102, 63 using Euclid's Algorithm?
Answer: For arbitrary numbers 668, 610, 102, 63 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.