Highest Common Factor of 814, 670, 47 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 814, 670, 47 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 814, 670, 47 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 814, 670, 47 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 814, 670, 47 is 1.
HCF(814, 670, 47) = 1
HCF of 814, 670, 47 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 814, 670, 47 is 1.
Highest Common Factor of 814,670,47 is 1
Step 1: Since 814 > 670, we apply the division lemma to 814 and 670, to get
814 = 670 x 1 + 144
Step 2: Since the reminder 670 ≠ 0, we apply division lemma to 144 and 670, to get
670 = 144 x 4 + 94
Step 3: We consider the new divisor 144 and the new remainder 94, and apply the division lemma to get
144 = 94 x 1 + 50
We consider the new divisor 94 and the new remainder 50,and apply the division lemma to get
94 = 50 x 1 + 44
We consider the new divisor 50 and the new remainder 44,and apply the division lemma to get
50 = 44 x 1 + 6
We consider the new divisor 44 and the new remainder 6,and apply the division lemma to get
44 = 6 x 7 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma 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 814 and 670 is 2
Notice that 2 = HCF(6,2) = HCF(44,6) = HCF(50,44) = HCF(94,50) = HCF(144,94) = HCF(670,144) = HCF(814,670) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 47 > 2, we apply the division lemma to 47 and 2, to get
47 = 2 x 23 + 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 47 is 1
Notice that 1 = HCF(2,1) = HCF(47,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 814, 670, 47 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 814, 670, 47?
Answer: HCF of 814, 670, 47 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 814, 670, 47 using Euclid's Algorithm?
Answer: For arbitrary numbers 814, 670, 47 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.