Highest Common Factor of 870, 686, 780 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 870, 686, 780 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 870, 686, 780 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 870, 686, 780 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 870, 686, 780 is 2.
HCF(870, 686, 780) = 2
HCF of 870, 686, 780 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 870, 686, 780 is 2.
Highest Common Factor of 870,686,780 is 2
Step 1: Since 870 > 686, we apply the division lemma to 870 and 686, to get
870 = 686 x 1 + 184
Step 2: Since the reminder 686 ≠ 0, we apply division lemma to 184 and 686, to get
686 = 184 x 3 + 134
Step 3: We consider the new divisor 184 and the new remainder 134, and apply the division lemma to get
184 = 134 x 1 + 50
We consider the new divisor 134 and the new remainder 50,and apply the division lemma to get
134 = 50 x 2 + 34
We consider the new divisor 50 and the new remainder 34,and apply the division lemma to get
50 = 34 x 1 + 16
We consider the new divisor 34 and the new remainder 16,and apply the division lemma to get
34 = 16 x 2 + 2
We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 870 and 686 is 2
Notice that 2 = HCF(16,2) = HCF(34,16) = HCF(50,34) = HCF(134,50) = HCF(184,134) = HCF(686,184) = HCF(870,686) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 780 > 2, we apply the division lemma to 780 and 2, to get
780 = 2 x 390 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 780 is 2
Notice that 2 = HCF(780,2) .
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Frequently Asked Questions on HCF of 870, 686, 780 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 870, 686, 780?
Answer: HCF of 870, 686, 780 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 870, 686, 780 using Euclid's Algorithm?
Answer: For arbitrary numbers 870, 686, 780 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.