Highest Common Factor of 578, 712, 294 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, 712, 294 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 578, 712, 294 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 578, 712, 294 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, 712, 294 is 2.
HCF(578, 712, 294) = 2
HCF of 578, 712, 294 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, 712, 294 is 2.
Highest Common Factor of 578,712,294 is 2
Step 1: Since 712 > 578, we apply the division lemma to 712 and 578, to get
712 = 578 x 1 + 134
Step 2: Since the reminder 578 ≠ 0, we apply division lemma to 134 and 578, to get
578 = 134 x 4 + 42
Step 3: We consider the new divisor 134 and the new remainder 42, and apply the division lemma to get
134 = 42 x 3 + 8
We consider the new divisor 42 and the new remainder 8,and apply the division lemma to get
42 = 8 x 5 + 2
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 578 and 712 is 2
Notice that 2 = HCF(8,2) = HCF(42,8) = HCF(134,42) = HCF(578,134) = HCF(712,578) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 294 > 2, we apply the division lemma to 294 and 2, to get
294 = 2 x 147 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 294 is 2
Notice that 2 = HCF(294,2) .
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Frequently Asked Questions on HCF of 578, 712, 294 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, 712, 294?
Answer: HCF of 578, 712, 294 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 578, 712, 294 using Euclid's Algorithm?
Answer: For arbitrary numbers 578, 712, 294 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.