Highest Common Factor of 416, 308, 681 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 416, 308, 681 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 416, 308, 681 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 416, 308, 681 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 416, 308, 681 is 1.
HCF(416, 308, 681) = 1
HCF of 416, 308, 681 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 416, 308, 681 is 1.
Highest Common Factor of 416,308,681 is 1
Step 1: Since 416 > 308, we apply the division lemma to 416 and 308, to get
416 = 308 x 1 + 108
Step 2: Since the reminder 308 ≠ 0, we apply division lemma to 108 and 308, to get
308 = 108 x 2 + 92
Step 3: We consider the new divisor 108 and the new remainder 92, and apply the division lemma to get
108 = 92 x 1 + 16
We consider the new divisor 92 and the new remainder 16,and apply the division lemma to get
92 = 16 x 5 + 12
We consider the new divisor 16 and the new remainder 12,and apply the division lemma to get
16 = 12 x 1 + 4
We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 416 and 308 is 4
Notice that 4 = HCF(12,4) = HCF(16,12) = HCF(92,16) = HCF(108,92) = HCF(308,108) = HCF(416,308) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 681 > 4, we apply the division lemma to 681 and 4, to get
681 = 4 x 170 + 1
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 681 is 1
Notice that 1 = HCF(4,1) = HCF(681,4) .
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Frequently Asked Questions on HCF of 416, 308, 681 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 416, 308, 681?
Answer: HCF of 416, 308, 681 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 416, 308, 681 using Euclid's Algorithm?
Answer: For arbitrary numbers 416, 308, 681 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
