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 378, 597, 368, 382 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 378, 597, 368, 382 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 378, 597, 368, 382 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 378, 597, 368, 382 is 1.
HCF(378, 597, 368, 382) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 378, 597, 368, 382 is 1.
Step 1: Since 597 > 378, we apply the division lemma to 597 and 378, to get
597 = 378 x 1 + 219
Step 2: Since the reminder 378 ≠ 0, we apply division lemma to 219 and 378, to get
378 = 219 x 1 + 159
Step 3: We consider the new divisor 219 and the new remainder 159, and apply the division lemma to get
219 = 159 x 1 + 60
We consider the new divisor 159 and the new remainder 60,and apply the division lemma to get
159 = 60 x 2 + 39
We consider the new divisor 60 and the new remainder 39,and apply the division lemma to get
60 = 39 x 1 + 21
We consider the new divisor 39 and the new remainder 21,and apply the division lemma to get
39 = 21 x 1 + 18
We consider the new divisor 21 and the new remainder 18,and apply the division lemma to get
21 = 18 x 1 + 3
We consider the new divisor 18 and the new remainder 3,and apply the division lemma to get
18 = 3 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 378 and 597 is 3
Notice that 3 = HCF(18,3) = HCF(21,18) = HCF(39,21) = HCF(60,39) = HCF(159,60) = HCF(219,159) = HCF(378,219) = HCF(597,378) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 368 > 3, we apply the division lemma to 368 and 3, to get
368 = 3 x 122 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 3 and 368 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(368,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 382 > 1, we apply the division lemma to 382 and 1, to get
382 = 1 x 382 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 382 is 1
Notice that 1 = HCF(382,1) .
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 378, 597, 368, 382?
Answer: HCF of 378, 597, 368, 382 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 378, 597, 368, 382 using Euclid's Algorithm?
Answer: For arbitrary numbers 378, 597, 368, 382 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.