Highest Common Factor of 420, 440, 454 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, 440, 454 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 420, 440, 454 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, 440, 454 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, 440, 454 is 2.
HCF(420, 440, 454) = 2
HCF of 420, 440, 454 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, 440, 454 is 2.
Highest Common Factor of 420,440,454 is 2
Step 1: Since 440 > 420, we apply the division lemma to 440 and 420, to get
440 = 420 x 1 + 20
Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 20 and 420, to get
420 = 20 x 21 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 420 and 440 is 20
Notice that 20 = HCF(420,20) = HCF(440,420) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 454 > 20, we apply the division lemma to 454 and 20, to get
454 = 20 x 22 + 14
Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 14 and 20, to get
20 = 14 x 1 + 6
Step 3: We consider the new divisor 14 and the new remainder 6, and apply the division lemma to get
14 = 6 x 2 + 2
We consider the new divisor 6 and the new remainder 2, and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 20 and 454 is 2
Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(20,14) = HCF(454,20) .
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Frequently Asked Questions on HCF of 420, 440, 454 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, 440, 454?
Answer: HCF of 420, 440, 454 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 420, 440, 454 using Euclid's Algorithm?
Answer: For arbitrary numbers 420, 440, 454 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.