Highest Common Factor of 65, 98, 80, 462 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 65, 98, 80, 462 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 65, 98, 80, 462 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 65, 98, 80, 462 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 65, 98, 80, 462 is 1.
HCF(65, 98, 80, 462) = 1
HCF of 65, 98, 80, 462 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 65, 98, 80, 462 is 1.
Highest Common Factor of 65,98,80,462 is 1
Step 1: Since 98 > 65, we apply the division lemma to 98 and 65, to get
98 = 65 x 1 + 33
Step 2: Since the reminder 65 ≠ 0, we apply division lemma to 33 and 65, to get
65 = 33 x 1 + 32
Step 3: We consider the new divisor 33 and the new remainder 32, and apply the division lemma to get
33 = 32 x 1 + 1
We consider the new divisor 32 and the new remainder 1, and apply the division lemma to get
32 = 1 x 32 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 65 and 98 is 1
Notice that 1 = HCF(32,1) = HCF(33,32) = HCF(65,33) = HCF(98,65) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 80 > 1, we apply the division lemma to 80 and 1, to get
80 = 1 x 80 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 80 is 1
Notice that 1 = HCF(80,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 462 > 1, we apply the division lemma to 462 and 1, to get
462 = 1 x 462 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 462 is 1
Notice that 1 = HCF(462,1) .
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Frequently Asked Questions on HCF of 65, 98, 80, 462 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 65, 98, 80, 462?
Answer: HCF of 65, 98, 80, 462 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 65, 98, 80, 462 using Euclid's Algorithm?
Answer: For arbitrary numbers 65, 98, 80, 462 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.