Highest Common Factor of 310, 470, 422 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 310, 470, 422 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 310, 470, 422 is 2 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 310, 470, 422 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 310, 470, 422 is 2.
HCF(310, 470, 422) = 2
HCF of 310, 470, 422 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 310, 470, 422 is 2.
Highest Common Factor of 310,470,422 is 2
Step 1: Since 470 > 310, we apply the division lemma to 470 and 310, to get
470 = 310 x 1 + 160
Step 2: Since the reminder 310 ≠ 0, we apply division lemma to 160 and 310, to get
310 = 160 x 1 + 150
Step 3: We consider the new divisor 160 and the new remainder 150, and apply the division lemma to get
160 = 150 x 1 + 10
We consider the new divisor 150 and the new remainder 10, and apply the division lemma to get
150 = 10 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 310 and 470 is 10
Notice that 10 = HCF(150,10) = HCF(160,150) = HCF(310,160) = HCF(470,310) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 422 > 10, we apply the division lemma to 422 and 10, to get
422 = 10 x 42 + 2
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 2 and 10, to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 10 and 422 is 2
Notice that 2 = HCF(10,2) = HCF(422,10) .
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Frequently Asked Questions on HCF of 310, 470, 422 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 310, 470, 422?
Answer: HCF of 310, 470, 422 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 310, 470, 422 using Euclid's Algorithm?
Answer: For arbitrary numbers 310, 470, 422 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.