Highest Common Factor of 688, 559, 414 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 688, 559, 414 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 688, 559, 414 is 1 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 688, 559, 414 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 688, 559, 414 is 1.
HCF(688, 559, 414) = 1
HCF of 688, 559, 414 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 688, 559, 414 is 1.
Highest Common Factor of 688,559,414 is 1
Step 1: Since 688 > 559, we apply the division lemma to 688 and 559, to get
688 = 559 x 1 + 129
Step 2: Since the reminder 559 ≠ 0, we apply division lemma to 129 and 559, to get
559 = 129 x 4 + 43
Step 3: We consider the new divisor 129 and the new remainder 43, and apply the division lemma to get
129 = 43 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 43, the HCF of 688 and 559 is 43
Notice that 43 = HCF(129,43) = HCF(559,129) = HCF(688,559) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 414 > 43, we apply the division lemma to 414 and 43, to get
414 = 43 x 9 + 27
Step 2: Since the reminder 43 ≠ 0, we apply division lemma to 27 and 43, to get
43 = 27 x 1 + 16
Step 3: We consider the new divisor 27 and the new remainder 16, and apply the division lemma to get
27 = 16 x 1 + 11
We consider the new divisor 16 and the new remainder 11,and apply the division lemma to get
16 = 11 x 1 + 5
We consider the new divisor 11 and the new remainder 5,and apply the division lemma to get
11 = 5 x 2 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 43 and 414 is 1
Notice that 1 = HCF(5,1) = HCF(11,5) = HCF(16,11) = HCF(27,16) = HCF(43,27) = HCF(414,43) .
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Frequently Asked Questions on HCF of 688, 559, 414 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 688, 559, 414?
Answer: HCF of 688, 559, 414 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 688, 559, 414 using Euclid's Algorithm?
Answer: For arbitrary numbers 688, 559, 414 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.