Highest Common Factor of 420, 920, 608 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, 920, 608 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 420, 920, 608 is 4 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, 920, 608 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, 920, 608 is 4.
HCF(420, 920, 608) = 4
HCF of 420, 920, 608 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, 920, 608 is 4.
Highest Common Factor of 420,920,608 is 4
Step 1: Since 920 > 420, we apply the division lemma to 920 and 420, to get
920 = 420 x 2 + 80
Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 80 and 420, to get
420 = 80 x 5 + 20
Step 3: We consider the new divisor 80 and the new remainder 20, and apply the division lemma to get
80 = 20 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 420 and 920 is 20
Notice that 20 = HCF(80,20) = HCF(420,80) = HCF(920,420) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 608 > 20, we apply the division lemma to 608 and 20, to get
608 = 20 x 30 + 8
Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 8 and 20, to get
20 = 8 x 2 + 4
Step 3: We consider the new divisor 8 and the new remainder 4, and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 20 and 608 is 4
Notice that 4 = HCF(8,4) = HCF(20,8) = HCF(608,20) .
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Frequently Asked Questions on HCF of 420, 920, 608 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, 920, 608?
Answer: HCF of 420, 920, 608 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 420, 920, 608 using Euclid's Algorithm?
Answer: For arbitrary numbers 420, 920, 608 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
