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, 621, 135 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 379, 621, 135 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, 621, 135 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, 621, 135 is 1.
HCF(379, 621, 135) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 379, 621, 135 is 1.
Step 1: Since 621 > 379, we apply the division lemma to 621 and 379, to get
621 = 379 x 1 + 242
Step 2: Since the reminder 379 ≠ 0, we apply division lemma to 242 and 379, to get
379 = 242 x 1 + 137
Step 3: We consider the new divisor 242 and the new remainder 137, and apply the division lemma to get
242 = 137 x 1 + 105
We consider the new divisor 137 and the new remainder 105,and apply the division lemma to get
137 = 105 x 1 + 32
We consider the new divisor 105 and the new remainder 32,and apply the division lemma to get
105 = 32 x 3 + 9
We consider the new divisor 32 and the new remainder 9,and apply the division lemma to get
32 = 9 x 3 + 5
We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get
9 = 5 x 1 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma 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 379 and 621 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(32,9) = HCF(105,32) = HCF(137,105) = HCF(242,137) = HCF(379,242) = HCF(621,379) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 135 > 1, we apply the division lemma to 135 and 1, to get
135 = 1 x 135 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 135 is 1
Notice that 1 = HCF(135,1) .
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, 621, 135?
Answer: HCF of 379, 621, 135 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 379, 621, 135 using Euclid's Algorithm?
Answer: For arbitrary numbers 379, 621, 135 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.