Highest Common Factor of 371, 967, 355 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 371, 967, 355 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 371, 967, 355 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 371, 967, 355 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 371, 967, 355 is 1.
HCF(371, 967, 355) = 1
HCF of 371, 967, 355 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 371, 967, 355 is 1.
Highest Common Factor of 371,967,355 is 1
Step 1: Since 967 > 371, we apply the division lemma to 967 and 371, to get
967 = 371 x 2 + 225
Step 2: Since the reminder 371 ≠ 0, we apply division lemma to 225 and 371, to get
371 = 225 x 1 + 146
Step 3: We consider the new divisor 225 and the new remainder 146, and apply the division lemma to get
225 = 146 x 1 + 79
We consider the new divisor 146 and the new remainder 79,and apply the division lemma to get
146 = 79 x 1 + 67
We consider the new divisor 79 and the new remainder 67,and apply the division lemma to get
79 = 67 x 1 + 12
We consider the new divisor 67 and the new remainder 12,and apply the division lemma to get
67 = 12 x 5 + 7
We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get
12 = 7 x 1 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 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 371 and 967 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(67,12) = HCF(79,67) = HCF(146,79) = HCF(225,146) = HCF(371,225) = HCF(967,371) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 355 > 1, we apply the division lemma to 355 and 1, to get
355 = 1 x 355 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 355 is 1
Notice that 1 = HCF(355,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 371, 967, 355 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 371, 967, 355?
Answer: HCF of 371, 967, 355 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 371, 967, 355 using Euclid's Algorithm?
Answer: For arbitrary numbers 371, 967, 355 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.