Highest Common Factor of 820, 472, 144 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 820, 472, 144 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 820, 472, 144 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 820, 472, 144 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 820, 472, 144 is 4.
HCF(820, 472, 144) = 4
HCF of 820, 472, 144 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 820, 472, 144 is 4.
Highest Common Factor of 820,472,144 is 4
Step 1: Since 820 > 472, we apply the division lemma to 820 and 472, to get
820 = 472 x 1 + 348
Step 2: Since the reminder 472 ≠ 0, we apply division lemma to 348 and 472, to get
472 = 348 x 1 + 124
Step 3: We consider the new divisor 348 and the new remainder 124, and apply the division lemma to get
348 = 124 x 2 + 100
We consider the new divisor 124 and the new remainder 100,and apply the division lemma to get
124 = 100 x 1 + 24
We consider the new divisor 100 and the new remainder 24,and apply the division lemma to get
100 = 24 x 4 + 4
We consider the new divisor 24 and the new remainder 4,and apply the division lemma to get
24 = 4 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 820 and 472 is 4
Notice that 4 = HCF(24,4) = HCF(100,24) = HCF(124,100) = HCF(348,124) = HCF(472,348) = HCF(820,472) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 144 > 4, we apply the division lemma to 144 and 4, to get
144 = 4 x 36 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 144 is 4
Notice that 4 = HCF(144,4) .
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Frequently Asked Questions on HCF of 820, 472, 144 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 820, 472, 144?
Answer: HCF of 820, 472, 144 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 820, 472, 144 using Euclid's Algorithm?
Answer: For arbitrary numbers 820, 472, 144 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
