Highest Common Factor of 500, 720, 188 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 500, 720, 188 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 500, 720, 188 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 500, 720, 188 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 500, 720, 188 is 4.
HCF(500, 720, 188) = 4
HCF of 500, 720, 188 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 500, 720, 188 is 4.
Highest Common Factor of 500,720,188 is 4
Step 1: Since 720 > 500, we apply the division lemma to 720 and 500, to get
720 = 500 x 1 + 220
Step 2: Since the reminder 500 ≠ 0, we apply division lemma to 220 and 500, to get
500 = 220 x 2 + 60
Step 3: We consider the new divisor 220 and the new remainder 60, and apply the division lemma to get
220 = 60 x 3 + 40
We consider the new divisor 60 and the new remainder 40,and apply the division lemma to get
60 = 40 x 1 + 20
We consider the new divisor 40 and the new remainder 20,and apply the division lemma to get
40 = 20 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 500 and 720 is 20
Notice that 20 = HCF(40,20) = HCF(60,40) = HCF(220,60) = HCF(500,220) = HCF(720,500) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 188 > 20, we apply the division lemma to 188 and 20, to get
188 = 20 x 9 + 8
Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 8 and 20, to get
20 = 8 x 2 + 4
Step 3: We consider the new divisor 8 and the new remainder 4, and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 20 and 188 is 4
Notice that 4 = HCF(8,4) = HCF(20,8) = HCF(188,20) .
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Frequently Asked Questions on HCF of 500, 720, 188 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 500, 720, 188?
Answer: HCF of 500, 720, 188 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 500, 720, 188 using Euclid's Algorithm?
Answer: For arbitrary numbers 500, 720, 188 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.