Highest Common Factor of 513, 190, 160, 85 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 513, 190, 160, 85 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 513, 190, 160, 85 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 513, 190, 160, 85 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 513, 190, 160, 85 is 1.
HCF(513, 190, 160, 85) = 1
HCF of 513, 190, 160, 85 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 513, 190, 160, 85 is 1.
Highest Common Factor of 513,190,160,85 is 1
Step 1: Since 513 > 190, we apply the division lemma to 513 and 190, to get
513 = 190 x 2 + 133
Step 2: Since the reminder 190 ≠ 0, we apply division lemma to 133 and 190, to get
190 = 133 x 1 + 57
Step 3: We consider the new divisor 133 and the new remainder 57, and apply the division lemma to get
133 = 57 x 2 + 19
We consider the new divisor 57 and the new remainder 19, and apply the division lemma to get
57 = 19 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 19, the HCF of 513 and 190 is 19
Notice that 19 = HCF(57,19) = HCF(133,57) = HCF(190,133) = HCF(513,190) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 160 > 19, we apply the division lemma to 160 and 19, to get
160 = 19 x 8 + 8
Step 2: Since the reminder 19 ≠ 0, we apply division lemma to 8 and 19, to get
19 = 8 x 2 + 3
Step 3: We consider the new divisor 8 and the new remainder 3, and apply the division lemma to get
8 = 3 x 2 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 19 and 160 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(19,8) = HCF(160,19) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 85 > 1, we apply the division lemma to 85 and 1, to get
85 = 1 x 85 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 85 is 1
Notice that 1 = HCF(85,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 513, 190, 160, 85 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 513, 190, 160, 85?
Answer: HCF of 513, 190, 160, 85 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 513, 190, 160, 85 using Euclid's Algorithm?
Answer: For arbitrary numbers 513, 190, 160, 85 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.