Highest Common Factor of 870, 786, 812, 42 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, 786, 812, 42 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 870, 786, 812, 42 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, 786, 812, 42 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, 786, 812, 42 is 2.
HCF(870, 786, 812, 42) = 2
HCF of 870, 786, 812, 42 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, 786, 812, 42 is 2.
Highest Common Factor of 870,786,812,42 is 2
Step 1: Since 870 > 786, we apply the division lemma to 870 and 786, to get
870 = 786 x 1 + 84
Step 2: Since the reminder 786 ≠ 0, we apply division lemma to 84 and 786, to get
786 = 84 x 9 + 30
Step 3: We consider the new divisor 84 and the new remainder 30, and apply the division lemma to get
84 = 30 x 2 + 24
We consider the new divisor 30 and the new remainder 24,and apply the division lemma to get
30 = 24 x 1 + 6
We consider the new divisor 24 and the new remainder 6,and apply the division lemma to get
24 = 6 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 870 and 786 is 6
Notice that 6 = HCF(24,6) = HCF(30,24) = HCF(84,30) = HCF(786,84) = HCF(870,786) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 812 > 6, we apply the division lemma to 812 and 6, to get
812 = 6 x 135 + 2
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 2 and 6, to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6 and 812 is 2
Notice that 2 = HCF(6,2) = HCF(812,6) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 42 > 2, we apply the division lemma to 42 and 2, to get
42 = 2 x 21 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 42 is 2
Notice that 2 = HCF(42,2) .
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Frequently Asked Questions on HCF of 870, 786, 812, 42 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, 786, 812, 42?
Answer: HCF of 870, 786, 812, 42 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 870, 786, 812, 42 using Euclid's Algorithm?
Answer: For arbitrary numbers 870, 786, 812, 42 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.