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 154, 675, 381 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 154, 675, 381 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 154, 675, 381 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 154, 675, 381 is 1.
HCF(154, 675, 381) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 154, 675, 381 is 1.
Step 1: Since 675 > 154, we apply the division lemma to 675 and 154, to get
675 = 154 x 4 + 59
Step 2: Since the reminder 154 ≠ 0, we apply division lemma to 59 and 154, to get
154 = 59 x 2 + 36
Step 3: We consider the new divisor 59 and the new remainder 36, and apply the division lemma to get
59 = 36 x 1 + 23
We consider the new divisor 36 and the new remainder 23,and apply the division lemma to get
36 = 23 x 1 + 13
We consider the new divisor 23 and the new remainder 13,and apply the division lemma to get
23 = 13 x 1 + 10
We consider the new divisor 13 and the new remainder 10,and apply the division lemma to get
13 = 10 x 1 + 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 154 and 675 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(23,13) = HCF(36,23) = HCF(59,36) = HCF(154,59) = HCF(675,154) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 381 > 1, we apply the division lemma to 381 and 1, to get
381 = 1 x 381 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 381 is 1
Notice that 1 = HCF(381,1) .
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 154, 675, 381?
Answer: HCF of 154, 675, 381 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 154, 675, 381 using Euclid's Algorithm?
Answer: For arbitrary numbers 154, 675, 381 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.