Highest Common Factor of 708, 870, 516, 797 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 708, 870, 516, 797 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 708, 870, 516, 797 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 708, 870, 516, 797 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 708, 870, 516, 797 is 1.
HCF(708, 870, 516, 797) = 1
HCF of 708, 870, 516, 797 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 708, 870, 516, 797 is 1.
Highest Common Factor of 708,870,516,797 is 1
Step 1: Since 870 > 708, we apply the division lemma to 870 and 708, to get
870 = 708 x 1 + 162
Step 2: Since the reminder 708 ≠ 0, we apply division lemma to 162 and 708, to get
708 = 162 x 4 + 60
Step 3: We consider the new divisor 162 and the new remainder 60, and apply the division lemma to get
162 = 60 x 2 + 42
We consider the new divisor 60 and the new remainder 42,and apply the division lemma to get
60 = 42 x 1 + 18
We consider the new divisor 42 and the new remainder 18,and apply the division lemma to get
42 = 18 x 2 + 6
We consider the new divisor 18 and the new remainder 6,and apply the division lemma to get
18 = 6 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 708 and 870 is 6
Notice that 6 = HCF(18,6) = HCF(42,18) = HCF(60,42) = HCF(162,60) = HCF(708,162) = HCF(870,708) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 516 > 6, we apply the division lemma to 516 and 6, to get
516 = 6 x 86 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 6 and 516 is 6
Notice that 6 = HCF(516,6) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 797 > 6, we apply the division lemma to 797 and 6, to get
797 = 6 x 132 + 5
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 5 and 6, to get
6 = 5 x 1 + 1
Step 3: We consider the new divisor 5 and the new remainder 1, and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 797 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(797,6) .
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Frequently Asked Questions on HCF of 708, 870, 516, 797 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 708, 870, 516, 797?
Answer: HCF of 708, 870, 516, 797 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 708, 870, 516, 797 using Euclid's Algorithm?
Answer: For arbitrary numbers 708, 870, 516, 797 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.