Highest Common Factor of 61, 222, 340 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 61, 222, 340 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 61, 222, 340 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 61, 222, 340 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 61, 222, 340 is 1.
HCF(61, 222, 340) = 1
HCF of 61, 222, 340 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 61, 222, 340 is 1.
Highest Common Factor of 61,222,340 is 1
Step 1: Since 222 > 61, we apply the division lemma to 222 and 61, to get
222 = 61 x 3 + 39
Step 2: Since the reminder 61 ≠ 0, we apply division lemma to 39 and 61, to get
61 = 39 x 1 + 22
Step 3: We consider the new divisor 39 and the new remainder 22, and apply the division lemma to get
39 = 22 x 1 + 17
We consider the new divisor 22 and the new remainder 17,and apply the division lemma to get
22 = 17 x 1 + 5
We consider the new divisor 17 and the new remainder 5,and apply the division lemma to get
17 = 5 x 3 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 61 and 222 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(17,5) = HCF(22,17) = HCF(39,22) = HCF(61,39) = HCF(222,61) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 340 > 1, we apply the division lemma to 340 and 1, to get
340 = 1 x 340 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 340 is 1
Notice that 1 = HCF(340,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 61, 222, 340 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 61, 222, 340?
Answer: HCF of 61, 222, 340 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 61, 222, 340 using Euclid's Algorithm?
Answer: For arbitrary numbers 61, 222, 340 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.