Highest Common Factor of 544, 752, 218 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 544, 752, 218 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 544, 752, 218 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 544, 752, 218 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 544, 752, 218 is 2.
HCF(544, 752, 218) = 2
HCF of 544, 752, 218 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 544, 752, 218 is 2.
Highest Common Factor of 544,752,218 is 2
Step 1: Since 752 > 544, we apply the division lemma to 752 and 544, to get
752 = 544 x 1 + 208
Step 2: Since the reminder 544 ≠ 0, we apply division lemma to 208 and 544, to get
544 = 208 x 2 + 128
Step 3: We consider the new divisor 208 and the new remainder 128, and apply the division lemma to get
208 = 128 x 1 + 80
We consider the new divisor 128 and the new remainder 80,and apply the division lemma to get
128 = 80 x 1 + 48
We consider the new divisor 80 and the new remainder 48,and apply the division lemma to get
80 = 48 x 1 + 32
We consider the new divisor 48 and the new remainder 32,and apply the division lemma to get
48 = 32 x 1 + 16
We consider the new divisor 32 and the new remainder 16,and apply the division lemma to get
32 = 16 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 544 and 752 is 16
Notice that 16 = HCF(32,16) = HCF(48,32) = HCF(80,48) = HCF(128,80) = HCF(208,128) = HCF(544,208) = HCF(752,544) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 218 > 16, we apply the division lemma to 218 and 16, to get
218 = 16 x 13 + 10
Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 10 and 16, to get
16 = 10 x 1 + 6
Step 3: We consider the new divisor 10 and the new remainder 6, and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 16 and 218 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(218,16) .
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Frequently Asked Questions on HCF of 544, 752, 218 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 544, 752, 218?
Answer: HCF of 544, 752, 218 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 544, 752, 218 using Euclid's Algorithm?
Answer: For arbitrary numbers 544, 752, 218 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.