Highest Common Factor of 301, 985, 67 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 301, 985, 67 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 301, 985, 67 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 301, 985, 67 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 301, 985, 67 is 1.
HCF(301, 985, 67) = 1
HCF of 301, 985, 67 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 301, 985, 67 is 1.
Highest Common Factor of 301,985,67 is 1
Step 1: Since 985 > 301, we apply the division lemma to 985 and 301, to get
985 = 301 x 3 + 82
Step 2: Since the reminder 301 ≠ 0, we apply division lemma to 82 and 301, to get
301 = 82 x 3 + 55
Step 3: We consider the new divisor 82 and the new remainder 55, and apply the division lemma to get
82 = 55 x 1 + 27
We consider the new divisor 55 and the new remainder 27,and apply the division lemma to get
55 = 27 x 2 + 1
We consider the new divisor 27 and the new remainder 1,and apply the division lemma to get
27 = 1 x 27 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 301 and 985 is 1
Notice that 1 = HCF(27,1) = HCF(55,27) = HCF(82,55) = HCF(301,82) = HCF(985,301) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 67 > 1, we apply the division lemma to 67 and 1, to get
67 = 1 x 67 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 67 is 1
Notice that 1 = HCF(67,1) .
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Frequently Asked Questions on HCF of 301, 985, 67 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 301, 985, 67?
Answer: HCF of 301, 985, 67 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 301, 985, 67 using Euclid's Algorithm?
Answer: For arbitrary numbers 301, 985, 67 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
