Highest Common Factor of 870, 782, 657 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, 782, 657 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 870, 782, 657 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 870, 782, 657 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, 782, 657 is 1.
HCF(870, 782, 657) = 1
HCF of 870, 782, 657 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, 782, 657 is 1.
Highest Common Factor of 870,782,657 is 1
Step 1: Since 870 > 782, we apply the division lemma to 870 and 782, to get
870 = 782 x 1 + 88
Step 2: Since the reminder 782 ≠ 0, we apply division lemma to 88 and 782, to get
782 = 88 x 8 + 78
Step 3: We consider the new divisor 88 and the new remainder 78, and apply the division lemma to get
88 = 78 x 1 + 10
We consider the new divisor 78 and the new remainder 10,and apply the division lemma to get
78 = 10 x 7 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 870 and 782 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(78,10) = HCF(88,78) = HCF(782,88) = HCF(870,782) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 657 > 2, we apply the division lemma to 657 and 2, to get
657 = 2 x 328 + 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 657 is 1
Notice that 1 = HCF(2,1) = HCF(657,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 870, 782, 657 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, 782, 657?
Answer: HCF of 870, 782, 657 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 870, 782, 657 using Euclid's Algorithm?
Answer: For arbitrary numbers 870, 782, 657 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.