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 385, 455, 192, 54 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 385, 455, 192, 54 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 385, 455, 192, 54 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 385, 455, 192, 54 is 1.
HCF(385, 455, 192, 54) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 385, 455, 192, 54 is 1.
Step 1: Since 455 > 385, we apply the division lemma to 455 and 385, to get
455 = 385 x 1 + 70
Step 2: Since the reminder 385 ≠ 0, we apply division lemma to 70 and 385, to get
385 = 70 x 5 + 35
Step 3: We consider the new divisor 70 and the new remainder 35, and apply the division lemma to get
70 = 35 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 35, the HCF of 385 and 455 is 35
Notice that 35 = HCF(70,35) = HCF(385,70) = HCF(455,385) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 192 > 35, we apply the division lemma to 192 and 35, to get
192 = 35 x 5 + 17
Step 2: Since the reminder 35 ≠ 0, we apply division lemma to 17 and 35, to get
35 = 17 x 2 + 1
Step 3: We consider the new divisor 17 and the new remainder 1, and apply the division lemma to get
17 = 1 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 35 and 192 is 1
Notice that 1 = HCF(17,1) = HCF(35,17) = HCF(192,35) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 54 > 1, we apply the division lemma to 54 and 1, to get
54 = 1 x 54 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 54 is 1
Notice that 1 = HCF(54,1) .
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 385, 455, 192, 54?
Answer: HCF of 385, 455, 192, 54 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 385, 455, 192, 54 using Euclid's Algorithm?
Answer: For arbitrary numbers 385, 455, 192, 54 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.