Highest Common Factor of 421, 6970 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 421, 6970 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 421, 6970 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 421, 6970 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 421, 6970 is 1.
HCF(421, 6970) = 1
HCF of 421, 6970 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 421, 6970 is 1.
Highest Common Factor of 421,6970 is 1
Step 1: Since 6970 > 421, we apply the division lemma to 6970 and 421, to get
6970 = 421 x 16 + 234
Step 2: Since the reminder 421 ≠ 0, we apply division lemma to 234 and 421, to get
421 = 234 x 1 + 187
Step 3: We consider the new divisor 234 and the new remainder 187, and apply the division lemma to get
234 = 187 x 1 + 47
We consider the new divisor 187 and the new remainder 47,and apply the division lemma to get
187 = 47 x 3 + 46
We consider the new divisor 47 and the new remainder 46,and apply the division lemma to get
47 = 46 x 1 + 1
We consider the new divisor 46 and the new remainder 1,and apply the division lemma to get
46 = 1 x 46 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 421 and 6970 is 1
Notice that 1 = HCF(46,1) = HCF(47,46) = HCF(187,47) = HCF(234,187) = HCF(421,234) = HCF(6970,421) .
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Frequently Asked Questions on HCF of 421, 6970 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 421, 6970?
Answer: HCF of 421, 6970 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 421, 6970 using Euclid's Algorithm?
Answer: For arbitrary numbers 421, 6970 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.