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 770, 132, 205 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 770, 132, 205 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 770, 132, 205 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 770, 132, 205 is 1.
HCF(770, 132, 205) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 770, 132, 205 is 1.
Step 1: Since 770 > 132, we apply the division lemma to 770 and 132, to get
770 = 132 x 5 + 110
Step 2: Since the reminder 132 ≠ 0, we apply division lemma to 110 and 132, to get
132 = 110 x 1 + 22
Step 3: We consider the new divisor 110 and the new remainder 22, and apply the division lemma to get
110 = 22 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 22, the HCF of 770 and 132 is 22
Notice that 22 = HCF(110,22) = HCF(132,110) = HCF(770,132) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 205 > 22, we apply the division lemma to 205 and 22, to get
205 = 22 x 9 + 7
Step 2: Since the reminder 22 ≠ 0, we apply division lemma to 7 and 22, to get
22 = 7 x 3 + 1
Step 3: We consider the new divisor 7 and the new remainder 1, and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 22 and 205 is 1
Notice that 1 = HCF(7,1) = HCF(22,7) = HCF(205,22) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 770, 132, 205?
Answer: HCF of 770, 132, 205 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 770, 132, 205 using Euclid's Algorithm?
Answer: For arbitrary numbers 770, 132, 205 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.