Highest Common Factor of 8024, 8160, 32779 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 8024, 8160, 32779 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8024, 8160, 32779 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 8024, 8160, 32779 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 8024, 8160, 32779 is 1.
HCF(8024, 8160, 32779) = 1
HCF of 8024, 8160, 32779 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8024, 8160, 32779 is 1.
Highest Common Factor of 8024,8160,32779 is 1
Step 1: Since 8160 > 8024, we apply the division lemma to 8160 and 8024, to get
8160 = 8024 x 1 + 136
Step 2: Since the reminder 8024 ≠ 0, we apply division lemma to 136 and 8024, to get
8024 = 136 x 59 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 136, the HCF of 8024 and 8160 is 136
Notice that 136 = HCF(8024,136) = HCF(8160,8024) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 32779 > 136, we apply the division lemma to 32779 and 136, to get
32779 = 136 x 241 + 3
Step 2: Since the reminder 136 ≠ 0, we apply division lemma to 3 and 136, to get
136 = 3 x 45 + 1
Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 136 and 32779 is 1
Notice that 1 = HCF(3,1) = HCF(136,3) = HCF(32779,136) .
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Frequently Asked Questions on HCF of 8024, 8160, 32779 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 8024, 8160, 32779?
Answer: HCF of 8024, 8160, 32779 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8024, 8160, 32779 using Euclid's Algorithm?
Answer: For arbitrary numbers 8024, 8160, 32779 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.