Highest Common Factor of 340, 890, 278 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, 890, 278 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 340, 890, 278 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, 890, 278 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, 890, 278 is 2.
HCF(340, 890, 278) = 2
HCF of 340, 890, 278 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, 890, 278 is 2.
Highest Common Factor of 340,890,278 is 2
Step 1: Since 890 > 340, we apply the division lemma to 890 and 340, to get
890 = 340 x 2 + 210
Step 2: Since the reminder 340 ≠ 0, we apply division lemma to 210 and 340, to get
340 = 210 x 1 + 130
Step 3: We consider the new divisor 210 and the new remainder 130, and apply the division lemma to get
210 = 130 x 1 + 80
We consider the new divisor 130 and the new remainder 80,and apply the division lemma to get
130 = 80 x 1 + 50
We consider the new divisor 80 and the new remainder 50,and apply the division lemma to get
80 = 50 x 1 + 30
We consider the new divisor 50 and the new remainder 30,and apply the division lemma to get
50 = 30 x 1 + 20
We consider the new divisor 30 and the new remainder 20,and apply the division lemma to get
30 = 20 x 1 + 10
We consider the new divisor 20 and the new remainder 10,and apply the division lemma to get
20 = 10 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 340 and 890 is 10
Notice that 10 = HCF(20,10) = HCF(30,20) = HCF(50,30) = HCF(80,50) = HCF(130,80) = HCF(210,130) = HCF(340,210) = HCF(890,340) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 278 > 10, we apply the division lemma to 278 and 10, to get
278 = 10 x 27 + 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 278 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(278,10) .
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Frequently Asked Questions on HCF of 340, 890, 278 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, 890, 278?
Answer: HCF of 340, 890, 278 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 340, 890, 278 using Euclid's Algorithm?
Answer: For arbitrary numbers 340, 890, 278 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.