Highest Common Factor of 340, 527, 488 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, 527, 488 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 340, 527, 488 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 340, 527, 488 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, 527, 488 is 1.
HCF(340, 527, 488) = 1
HCF of 340, 527, 488 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, 527, 488 is 1.
Highest Common Factor of 340,527,488 is 1
Step 1: Since 527 > 340, we apply the division lemma to 527 and 340, to get
527 = 340 x 1 + 187
Step 2: Since the reminder 340 ≠ 0, we apply division lemma to 187 and 340, to get
340 = 187 x 1 + 153
Step 3: We consider the new divisor 187 and the new remainder 153, and apply the division lemma to get
187 = 153 x 1 + 34
We consider the new divisor 153 and the new remainder 34,and apply the division lemma to get
153 = 34 x 4 + 17
We consider the new divisor 34 and the new remainder 17,and apply the division lemma to get
34 = 17 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 17, the HCF of 340 and 527 is 17
Notice that 17 = HCF(34,17) = HCF(153,34) = HCF(187,153) = HCF(340,187) = HCF(527,340) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 488 > 17, we apply the division lemma to 488 and 17, to get
488 = 17 x 28 + 12
Step 2: Since the reminder 17 ≠ 0, we apply division lemma to 12 and 17, to get
17 = 12 x 1 + 5
Step 3: We consider the new divisor 12 and the new remainder 5, and apply the division lemma to get
12 = 5 x 2 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 17 and 488 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(17,12) = HCF(488,17) .
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Frequently Asked Questions on HCF of 340, 527, 488 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, 527, 488?
Answer: HCF of 340, 527, 488 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 340, 527, 488 using Euclid's Algorithm?
Answer: For arbitrary numbers 340, 527, 488 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.