Highest Common Factor of 340, 870, 228 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 340, 870, 228 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 340, 870, 228 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 340, 870, 228 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 340, 870, 228 is 2.
HCF(340, 870, 228) = 2
HCF of 340, 870, 228 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 340, 870, 228 is 2.
Highest Common Factor of 340,870,228 is 2
Step 1: Since 870 > 340, we apply the division lemma to 870 and 340, to get
870 = 340 x 2 + 190
Step 2: Since the reminder 340 ≠ 0, we apply division lemma to 190 and 340, to get
340 = 190 x 1 + 150
Step 3: We consider the new divisor 190 and the new remainder 150, and apply the division lemma to get
190 = 150 x 1 + 40
We consider the new divisor 150 and the new remainder 40,and apply the division lemma to get
150 = 40 x 3 + 30
We consider the new divisor 40 and the new remainder 30,and apply the division lemma to get
40 = 30 x 1 + 10
We consider the new divisor 30 and the new remainder 10,and apply the division lemma to get
30 = 10 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 340 and 870 is 10
Notice that 10 = HCF(30,10) = HCF(40,30) = HCF(150,40) = HCF(190,150) = HCF(340,190) = HCF(870,340) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 228 > 10, we apply the division lemma to 228 and 10, to get
228 = 10 x 22 + 8
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 8 and 10, to get
10 = 8 x 1 + 2
Step 3: 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 10 and 228 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(228,10) .
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Frequently Asked Questions on HCF of 340, 870, 228 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 340, 870, 228?
Answer: HCF of 340, 870, 228 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 340, 870, 228 using Euclid's Algorithm?
Answer: For arbitrary numbers 340, 870, 228 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.