Highest Common Factor of 660, 735, 500 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 660, 735, 500 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 660, 735, 500 is 5 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 660, 735, 500 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 660, 735, 500 is 5.
HCF(660, 735, 500) = 5
HCF of 660, 735, 500 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 660, 735, 500 is 5.
Highest Common Factor of 660,735,500 is 5
Step 1: Since 735 > 660, we apply the division lemma to 735 and 660, to get
735 = 660 x 1 + 75
Step 2: Since the reminder 660 ≠ 0, we apply division lemma to 75 and 660, to get
660 = 75 x 8 + 60
Step 3: We consider the new divisor 75 and the new remainder 60, and apply the division lemma to get
75 = 60 x 1 + 15
We consider the new divisor 60 and the new remainder 15, and apply the division lemma to get
60 = 15 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 660 and 735 is 15
Notice that 15 = HCF(60,15) = HCF(75,60) = HCF(660,75) = HCF(735,660) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 500 > 15, we apply the division lemma to 500 and 15, to get
500 = 15 x 33 + 5
Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 5 and 15, to get
15 = 5 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 15 and 500 is 5
Notice that 5 = HCF(15,5) = HCF(500,15) .
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Frequently Asked Questions on HCF of 660, 735, 500 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 660, 735, 500?
Answer: HCF of 660, 735, 500 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 660, 735, 500 using Euclid's Algorithm?
Answer: For arbitrary numbers 660, 735, 500 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
