Highest Common Factor of 420, 718 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 420, 718 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 420, 718 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 420, 718 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 420, 718 is 2.
HCF(420, 718) = 2
HCF of 420, 718 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 420, 718 is 2.
Highest Common Factor of 420,718 is 2
Step 1: Since 718 > 420, we apply the division lemma to 718 and 420, to get
718 = 420 x 1 + 298
Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 298 and 420, to get
420 = 298 x 1 + 122
Step 3: We consider the new divisor 298 and the new remainder 122, and apply the division lemma to get
298 = 122 x 2 + 54
We consider the new divisor 122 and the new remainder 54,and apply the division lemma to get
122 = 54 x 2 + 14
We consider the new divisor 54 and the new remainder 14,and apply the division lemma to get
54 = 14 x 3 + 12
We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get
14 = 12 x 1 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 420 and 718 is 2
Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(54,14) = HCF(122,54) = HCF(298,122) = HCF(420,298) = HCF(718,420) .
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Frequently Asked Questions on HCF of 420, 718 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 420, 718?
Answer: HCF of 420, 718 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 420, 718 using Euclid's Algorithm?
Answer: For arbitrary numbers 420, 718 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.