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 379, 903, 506 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 379, 903, 506 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 379, 903, 506 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 379, 903, 506 is 1.
HCF(379, 903, 506) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 379, 903, 506 is 1.
Step 1: Since 903 > 379, we apply the division lemma to 903 and 379, to get
903 = 379 x 2 + 145
Step 2: Since the reminder 379 ≠ 0, we apply division lemma to 145 and 379, to get
379 = 145 x 2 + 89
Step 3: We consider the new divisor 145 and the new remainder 89, and apply the division lemma to get
145 = 89 x 1 + 56
We consider the new divisor 89 and the new remainder 56,and apply the division lemma to get
89 = 56 x 1 + 33
We consider the new divisor 56 and the new remainder 33,and apply the division lemma to get
56 = 33 x 1 + 23
We consider the new divisor 33 and the new remainder 23,and apply the division lemma to get
33 = 23 x 1 + 10
We consider the new divisor 23 and the new remainder 10,and apply the division lemma to get
23 = 10 x 2 + 3
We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get
10 = 3 x 3 + 1
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 379 and 903 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(23,10) = HCF(33,23) = HCF(56,33) = HCF(89,56) = HCF(145,89) = HCF(379,145) = HCF(903,379) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 506 > 1, we apply the division lemma to 506 and 1, to get
506 = 1 x 506 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 506 is 1
Notice that 1 = HCF(506,1) .
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 379, 903, 506?
Answer: HCF of 379, 903, 506 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 379, 903, 506 using Euclid's Algorithm?
Answer: For arbitrary numbers 379, 903, 506 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.