Highest Common Factor of 85, 52, 61, 135 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 85, 52, 61, 135 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 85, 52, 61, 135 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 85, 52, 61, 135 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 85, 52, 61, 135 is 1.
HCF(85, 52, 61, 135) = 1
HCF of 85, 52, 61, 135 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 85, 52, 61, 135 is 1.
Highest Common Factor of 85,52,61,135 is 1
Step 1: Since 85 > 52, we apply the division lemma to 85 and 52, to get
85 = 52 x 1 + 33
Step 2: Since the reminder 52 ≠ 0, we apply division lemma to 33 and 52, to get
52 = 33 x 1 + 19
Step 3: We consider the new divisor 33 and the new remainder 19, and apply the division lemma to get
33 = 19 x 1 + 14
We consider the new divisor 19 and the new remainder 14,and apply the division lemma to get
19 = 14 x 1 + 5
We consider the new divisor 14 and the new remainder 5,and apply the division lemma to get
14 = 5 x 2 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 85 and 52 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(19,14) = HCF(33,19) = HCF(52,33) = HCF(85,52) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 61 > 1, we apply the division lemma to 61 and 1, to get
61 = 1 x 61 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 61 is 1
Notice that 1 = HCF(61,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 135 > 1, we apply the division lemma to 135 and 1, to get
135 = 1 x 135 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 135 is 1
Notice that 1 = HCF(135,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 85, 52, 61, 135 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 85, 52, 61, 135?
Answer: HCF of 85, 52, 61, 135 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 85, 52, 61, 135 using Euclid's Algorithm?
Answer: For arbitrary numbers 85, 52, 61, 135 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.