Highest Common Factor of 144, 820, 973, 428 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 144, 820, 973, 428 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 144, 820, 973, 428 is 1 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 144, 820, 973, 428 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 144, 820, 973, 428 is 1.
HCF(144, 820, 973, 428) = 1
HCF of 144, 820, 973, 428 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 144, 820, 973, 428 is 1.
Highest Common Factor of 144,820,973,428 is 1
Step 1: Since 820 > 144, we apply the division lemma to 820 and 144, to get
820 = 144 x 5 + 100
Step 2: Since the reminder 144 ≠ 0, we apply division lemma to 100 and 144, to get
144 = 100 x 1 + 44
Step 3: We consider the new divisor 100 and the new remainder 44, and apply the division lemma to get
100 = 44 x 2 + 12
We consider the new divisor 44 and the new remainder 12,and apply the division lemma to get
44 = 12 x 3 + 8
We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get
12 = 8 x 1 + 4
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 144 and 820 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(44,12) = HCF(100,44) = HCF(144,100) = HCF(820,144) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 973 > 4, we apply the division lemma to 973 and 4, to get
973 = 4 x 243 + 1
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 973 is 1
Notice that 1 = HCF(4,1) = HCF(973,4) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 428 > 1, we apply the division lemma to 428 and 1, to get
428 = 1 x 428 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 428 is 1
Notice that 1 = HCF(428,1) .
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Frequently Asked Questions on HCF of 144, 820, 973, 428 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 144, 820, 973, 428?
Answer: HCF of 144, 820, 973, 428 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 144, 820, 973, 428 using Euclid's Algorithm?
Answer: For arbitrary numbers 144, 820, 973, 428 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.