Highest Common Factor of 680, 416, 815 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 680, 416, 815 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 680, 416, 815 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 680, 416, 815 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 680, 416, 815 is 1.
HCF(680, 416, 815) = 1
HCF of 680, 416, 815 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 680, 416, 815 is 1.
Highest Common Factor of 680,416,815 is 1
Step 1: Since 680 > 416, we apply the division lemma to 680 and 416, to get
680 = 416 x 1 + 264
Step 2: Since the reminder 416 ≠ 0, we apply division lemma to 264 and 416, to get
416 = 264 x 1 + 152
Step 3: We consider the new divisor 264 and the new remainder 152, and apply the division lemma to get
264 = 152 x 1 + 112
We consider the new divisor 152 and the new remainder 112,and apply the division lemma to get
152 = 112 x 1 + 40
We consider the new divisor 112 and the new remainder 40,and apply the division lemma to get
112 = 40 x 2 + 32
We consider the new divisor 40 and the new remainder 32,and apply the division lemma to get
40 = 32 x 1 + 8
We consider the new divisor 32 and the new remainder 8,and apply the division lemma to get
32 = 8 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 680 and 416 is 8
Notice that 8 = HCF(32,8) = HCF(40,32) = HCF(112,40) = HCF(152,112) = HCF(264,152) = HCF(416,264) = HCF(680,416) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 815 > 8, we apply the division lemma to 815 and 8, to get
815 = 8 x 101 + 7
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 7 and 8, to get
8 = 7 x 1 + 1
Step 3: We consider the new divisor 7 and the new remainder 1, and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8 and 815 is 1
Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(815,8) .
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Frequently Asked Questions on HCF of 680, 416, 815 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 680, 416, 815?
Answer: HCF of 680, 416, 815 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 680, 416, 815 using Euclid's Algorithm?
Answer: For arbitrary numbers 680, 416, 815 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.