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 364, 588, 362 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 364, 588, 362 is 2 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 364, 588, 362 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 364, 588, 362 is 2.
HCF(364, 588, 362) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 364, 588, 362 is 2.
Step 1: Since 588 > 364, we apply the division lemma to 588 and 364, to get
588 = 364 x 1 + 224
Step 2: Since the reminder 364 ≠ 0, we apply division lemma to 224 and 364, to get
364 = 224 x 1 + 140
Step 3: We consider the new divisor 224 and the new remainder 140, and apply the division lemma to get
224 = 140 x 1 + 84
We consider the new divisor 140 and the new remainder 84,and apply the division lemma to get
140 = 84 x 1 + 56
We consider the new divisor 84 and the new remainder 56,and apply the division lemma to get
84 = 56 x 1 + 28
We consider the new divisor 56 and the new remainder 28,and apply the division lemma to get
56 = 28 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 28, the HCF of 364 and 588 is 28
Notice that 28 = HCF(56,28) = HCF(84,56) = HCF(140,84) = HCF(224,140) = HCF(364,224) = HCF(588,364) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 362 > 28, we apply the division lemma to 362 and 28, to get
362 = 28 x 12 + 26
Step 2: Since the reminder 28 ≠ 0, we apply division lemma to 26 and 28, to get
28 = 26 x 1 + 2
Step 3: We consider the new divisor 26 and the new remainder 2, and apply the division lemma to get
26 = 2 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 28 and 362 is 2
Notice that 2 = HCF(26,2) = HCF(28,26) = HCF(362,28) .
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 364, 588, 362?
Answer: HCF of 364, 588, 362 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 364, 588, 362 using Euclid's Algorithm?
Answer: For arbitrary numbers 364, 588, 362 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.