Highest Common Factor of 755, 915, 66 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 755, 915, 66 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 755, 915, 66 is 1 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 755, 915, 66 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 755, 915, 66 is 1.
HCF(755, 915, 66) = 1
HCF of 755, 915, 66 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 755, 915, 66 is 1.
Highest Common Factor of 755,915,66 is 1
Step 1: Since 915 > 755, we apply the division lemma to 915 and 755, to get
915 = 755 x 1 + 160
Step 2: Since the reminder 755 ≠ 0, we apply division lemma to 160 and 755, to get
755 = 160 x 4 + 115
Step 3: We consider the new divisor 160 and the new remainder 115, and apply the division lemma to get
160 = 115 x 1 + 45
We consider the new divisor 115 and the new remainder 45,and apply the division lemma to get
115 = 45 x 2 + 25
We consider the new divisor 45 and the new remainder 25,and apply the division lemma to get
45 = 25 x 1 + 20
We consider the new divisor 25 and the new remainder 20,and apply the division lemma to get
25 = 20 x 1 + 5
We consider the new divisor 20 and the new remainder 5,and apply the division lemma to get
20 = 5 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 755 and 915 is 5
Notice that 5 = HCF(20,5) = HCF(25,20) = HCF(45,25) = HCF(115,45) = HCF(160,115) = HCF(755,160) = HCF(915,755) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 66 > 5, we apply the division lemma to 66 and 5, to get
66 = 5 x 13 + 1
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 66 is 1
Notice that 1 = HCF(5,1) = HCF(66,5) .
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Frequently Asked Questions on HCF of 755, 915, 66 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 755, 915, 66?
Answer: HCF of 755, 915, 66 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 755, 915, 66 using Euclid's Algorithm?
Answer: For arbitrary numbers 755, 915, 66 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.