Highest Common Factor of 220, 1780, 8424 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 220, 1780, 8424 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 220, 1780, 8424 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 220, 1780, 8424 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 220, 1780, 8424 is 4.
HCF(220, 1780, 8424) = 4
HCF of 220, 1780, 8424 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 220, 1780, 8424 is 4.
Highest Common Factor of 220,1780,8424 is 4
Step 1: Since 1780 > 220, we apply the division lemma to 1780 and 220, to get
1780 = 220 x 8 + 20
Step 2: Since the reminder 220 ≠ 0, we apply division lemma to 20 and 220, to get
220 = 20 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 220 and 1780 is 20
Notice that 20 = HCF(220,20) = HCF(1780,220) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8424 > 20, we apply the division lemma to 8424 and 20, to get
8424 = 20 x 421 + 4
Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 4 and 20, to get
20 = 4 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 20 and 8424 is 4
Notice that 4 = HCF(20,4) = HCF(8424,20) .
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Frequently Asked Questions on HCF of 220, 1780, 8424 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 220, 1780, 8424?
Answer: HCF of 220, 1780, 8424 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 220, 1780, 8424 using Euclid's Algorithm?
Answer: For arbitrary numbers 220, 1780, 8424 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.