Highest Common Factor of 578, 340, 680 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 578, 340, 680 i.e. 34 the largest integer that leaves a remainder zero for all numbers.
HCF of 578, 340, 680 is 34 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 578, 340, 680 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 578, 340, 680 is 34.
HCF(578, 340, 680) = 34
HCF of 578, 340, 680 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 578, 340, 680 is 34.
Highest Common Factor of 578,340,680 is 34
Step 1: Since 578 > 340, we apply the division lemma to 578 and 340, to get
578 = 340 x 1 + 238
Step 2: Since the reminder 340 ≠ 0, we apply division lemma to 238 and 340, to get
340 = 238 x 1 + 102
Step 3: We consider the new divisor 238 and the new remainder 102, and apply the division lemma to get
238 = 102 x 2 + 34
We consider the new divisor 102 and the new remainder 34, and apply the division lemma to get
102 = 34 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 34, the HCF of 578 and 340 is 34
Notice that 34 = HCF(102,34) = HCF(238,102) = HCF(340,238) = HCF(578,340) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 680 > 34, we apply the division lemma to 680 and 34, to get
680 = 34 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 34, the HCF of 34 and 680 is 34
Notice that 34 = HCF(680,34) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 578, 340, 680 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 578, 340, 680?
Answer: HCF of 578, 340, 680 is 34 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 578, 340, 680 using Euclid's Algorithm?
Answer: For arbitrary numbers 578, 340, 680 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.