Highest Common Factor of 345, 961, 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 345, 961, 85 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 345, 961, 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 345, 961, 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 345, 961, 85 is 1.
HCF(345, 961, 85) = 1
HCF of 345, 961, 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 345, 961, 85 is 1.
Highest Common Factor of 345,961,85 is 1
Step 1: Since 961 > 345, we apply the division lemma to 961 and 345, to get
961 = 345 x 2 + 271
Step 2: Since the reminder 345 ≠ 0, we apply division lemma to 271 and 345, to get
345 = 271 x 1 + 74
Step 3: We consider the new divisor 271 and the new remainder 74, and apply the division lemma to get
271 = 74 x 3 + 49
We consider the new divisor 74 and the new remainder 49,and apply the division lemma to get
74 = 49 x 1 + 25
We consider the new divisor 49 and the new remainder 25,and apply the division lemma to get
49 = 25 x 1 + 24
We consider the new divisor 25 and the new remainder 24,and apply the division lemma to get
25 = 24 x 1 + 1
We consider the new divisor 24 and the new remainder 1,and apply the division lemma to get
24 = 1 x 24 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 345 and 961 is 1
Notice that 1 = HCF(24,1) = HCF(25,24) = HCF(49,25) = HCF(74,49) = HCF(271,74) = HCF(345,271) = HCF(961,345) .
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 345, 961, 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 345, 961, 85?
Answer: HCF of 345, 961, 85 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 345, 961, 85 using Euclid's Algorithm?
Answer: For arbitrary numbers 345, 961, 85 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.