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 428, 580, 503, 21 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 428, 580, 503, 21 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 428, 580, 503, 21 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 428, 580, 503, 21 is 1.
HCF(428, 580, 503, 21) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 428, 580, 503, 21 is 1.
Step 1: Since 580 > 428, we apply the division lemma to 580 and 428, to get
580 = 428 x 1 + 152
Step 2: Since the reminder 428 ≠ 0, we apply division lemma to 152 and 428, to get
428 = 152 x 2 + 124
Step 3: We consider the new divisor 152 and the new remainder 124, and apply the division lemma to get
152 = 124 x 1 + 28
We consider the new divisor 124 and the new remainder 28,and apply the division lemma to get
124 = 28 x 4 + 12
We consider the new divisor 28 and the new remainder 12,and apply the division lemma to get
28 = 12 x 2 + 4
We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 428 and 580 is 4
Notice that 4 = HCF(12,4) = HCF(28,12) = HCF(124,28) = HCF(152,124) = HCF(428,152) = HCF(580,428) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 503 > 4, we apply the division lemma to 503 and 4, to get
503 = 4 x 125 + 3
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get
4 = 3 x 1 + 1
Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 503 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(503,4) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 21 > 1, we apply the division lemma to 21 and 1, to get
21 = 1 x 21 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 21 is 1
Notice that 1 = HCF(21,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 428, 580, 503, 21?
Answer: HCF of 428, 580, 503, 21 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 428, 580, 503, 21 using Euclid's Algorithm?
Answer: For arbitrary numbers 428, 580, 503, 21 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.