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 506, 868, 503 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 506, 868, 503 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 506, 868, 503 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 506, 868, 503 is 1.
HCF(506, 868, 503) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 506, 868, 503 is 1.
Step 1: Since 868 > 506, we apply the division lemma to 868 and 506, to get
868 = 506 x 1 + 362
Step 2: Since the reminder 506 ≠ 0, we apply division lemma to 362 and 506, to get
506 = 362 x 1 + 144
Step 3: We consider the new divisor 362 and the new remainder 144, and apply the division lemma to get
362 = 144 x 2 + 74
We consider the new divisor 144 and the new remainder 74,and apply the division lemma to get
144 = 74 x 1 + 70
We consider the new divisor 74 and the new remainder 70,and apply the division lemma to get
74 = 70 x 1 + 4
We consider the new divisor 70 and the new remainder 4,and apply the division lemma to get
70 = 4 x 17 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 506 and 868 is 2
Notice that 2 = HCF(4,2) = HCF(70,4) = HCF(74,70) = HCF(144,74) = HCF(362,144) = HCF(506,362) = HCF(868,506) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 503 > 2, we apply the division lemma to 503 and 2, to get
503 = 2 x 251 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 503 is 1
Notice that 1 = HCF(2,1) = HCF(503,2) .
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 506, 868, 503?
Answer: HCF of 506, 868, 503 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 506, 868, 503 using Euclid's Algorithm?
Answer: For arbitrary numbers 506, 868, 503 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.