Highest Common Factor of 434, 708, 588 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 434, 708, 588 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 434, 708, 588 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 434, 708, 588 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 434, 708, 588 is 2.
HCF(434, 708, 588) = 2
HCF of 434, 708, 588 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 434, 708, 588 is 2.
Highest Common Factor of 434,708,588 is 2
Step 1: Since 708 > 434, we apply the division lemma to 708 and 434, to get
708 = 434 x 1 + 274
Step 2: Since the reminder 434 ≠ 0, we apply division lemma to 274 and 434, to get
434 = 274 x 1 + 160
Step 3: We consider the new divisor 274 and the new remainder 160, and apply the division lemma to get
274 = 160 x 1 + 114
We consider the new divisor 160 and the new remainder 114,and apply the division lemma to get
160 = 114 x 1 + 46
We consider the new divisor 114 and the new remainder 46,and apply the division lemma to get
114 = 46 x 2 + 22
We consider the new divisor 46 and the new remainder 22,and apply the division lemma to get
46 = 22 x 2 + 2
We consider the new divisor 22 and the new remainder 2,and apply the division lemma to get
22 = 2 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 434 and 708 is 2
Notice that 2 = HCF(22,2) = HCF(46,22) = HCF(114,46) = HCF(160,114) = HCF(274,160) = HCF(434,274) = HCF(708,434) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 588 > 2, we apply the division lemma to 588 and 2, to get
588 = 2 x 294 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 588 is 2
Notice that 2 = HCF(588,2) .
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Frequently Asked Questions on HCF of 434, 708, 588 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 434, 708, 588?
Answer: HCF of 434, 708, 588 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 434, 708, 588 using Euclid's Algorithm?
Answer: For arbitrary numbers 434, 708, 588 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.