Highest Common Factor of 654, 982, 345, 52 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 654, 982, 345, 52 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 654, 982, 345, 52 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 654, 982, 345, 52 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 654, 982, 345, 52 is 1.
HCF(654, 982, 345, 52) = 1
HCF of 654, 982, 345, 52 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 654, 982, 345, 52 is 1.
Highest Common Factor of 654,982,345,52 is 1
Step 1: Since 982 > 654, we apply the division lemma to 982 and 654, to get
982 = 654 x 1 + 328
Step 2: Since the reminder 654 ≠ 0, we apply division lemma to 328 and 654, to get
654 = 328 x 1 + 326
Step 3: We consider the new divisor 328 and the new remainder 326, and apply the division lemma to get
328 = 326 x 1 + 2
We consider the new divisor 326 and the new remainder 2, and apply the division lemma to get
326 = 2 x 163 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 654 and 982 is 2
Notice that 2 = HCF(326,2) = HCF(328,326) = HCF(654,328) = HCF(982,654) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 345 > 2, we apply the division lemma to 345 and 2, to get
345 = 2 x 172 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 345 is 1
Notice that 1 = HCF(2,1) = HCF(345,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 52 > 1, we apply the division lemma to 52 and 1, to get
52 = 1 x 52 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 52 is 1
Notice that 1 = HCF(52,1) .
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Frequently Asked Questions on HCF of 654, 982, 345, 52 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 654, 982, 345, 52?
Answer: HCF of 654, 982, 345, 52 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 654, 982, 345, 52 using Euclid's Algorithm?
Answer: For arbitrary numbers 654, 982, 345, 52 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.