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 476, 371, 85 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 476, 371, 85 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 476, 371, 85 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 476, 371, 85 is 1.
HCF(476, 371, 85) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 476, 371, 85 is 1.
Step 1: Since 476 > 371, we apply the division lemma to 476 and 371, to get
476 = 371 x 1 + 105
Step 2: Since the reminder 371 ≠ 0, we apply division lemma to 105 and 371, to get
371 = 105 x 3 + 56
Step 3: We consider the new divisor 105 and the new remainder 56, and apply the division lemma to get
105 = 56 x 1 + 49
We consider the new divisor 56 and the new remainder 49,and apply the division lemma to get
56 = 49 x 1 + 7
We consider the new divisor 49 and the new remainder 7,and apply the division lemma to get
49 = 7 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 476 and 371 is 7
Notice that 7 = HCF(49,7) = HCF(56,49) = HCF(105,56) = HCF(371,105) = HCF(476,371) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 85 > 7, we apply the division lemma to 85 and 7, to get
85 = 7 x 12 + 1
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 1 and 7, to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7 and 85 is 1
Notice that 1 = HCF(7,1) = HCF(85,7) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 476, 371, 85?
Answer: HCF of 476, 371, 85 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 476, 371, 85 using Euclid's Algorithm?
Answer: For arbitrary numbers 476, 371, 85 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.