Highest Common Factor of 364, 440, 216 using Euclid's algorithm
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, 440, 216 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 364, 440, 216 is 4 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, 440, 216 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, 440, 216 is 4.
HCF(364, 440, 216) = 4
HCF of 364, 440, 216 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 364, 440, 216 is 4.
Highest Common Factor of 364,440,216 is 4
Step 1: Since 440 > 364, we apply the division lemma to 440 and 364, to get
440 = 364 x 1 + 76
Step 2: Since the reminder 364 ≠ 0, we apply division lemma to 76 and 364, to get
364 = 76 x 4 + 60
Step 3: We consider the new divisor 76 and the new remainder 60, and apply the division lemma to get
76 = 60 x 1 + 16
We consider the new divisor 60 and the new remainder 16,and apply the division lemma to get
60 = 16 x 3 + 12
We consider the new divisor 16 and the new remainder 12,and apply the division lemma to get
16 = 12 x 1 + 4
We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 364 and 440 is 4
Notice that 4 = HCF(12,4) = HCF(16,12) = HCF(60,16) = HCF(76,60) = HCF(364,76) = HCF(440,364) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 216 > 4, we apply the division lemma to 216 and 4, to get
216 = 4 x 54 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 216 is 4
Notice that 4 = HCF(216,4) .
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Frequently Asked Questions on HCF of 364, 440, 216 using Euclid's Algorithm
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, 440, 216?
Answer: HCF of 364, 440, 216 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 364, 440, 216 using Euclid's Algorithm?
Answer: For arbitrary numbers 364, 440, 216 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.