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, 985, 270 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 770, 985, 270 is 5 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, 985, 270 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, 985, 270 is 5.
HCF(770, 985, 270) = 5
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 770, 985, 270 is 5.
Step 1: Since 985 > 770, we apply the division lemma to 985 and 770, to get
985 = 770 x 1 + 215
Step 2: Since the reminder 770 ≠ 0, we apply division lemma to 215 and 770, to get
770 = 215 x 3 + 125
Step 3: We consider the new divisor 215 and the new remainder 125, and apply the division lemma to get
215 = 125 x 1 + 90
We consider the new divisor 125 and the new remainder 90,and apply the division lemma to get
125 = 90 x 1 + 35
We consider the new divisor 90 and the new remainder 35,and apply the division lemma to get
90 = 35 x 2 + 20
We consider the new divisor 35 and the new remainder 20,and apply the division lemma to get
35 = 20 x 1 + 15
We consider the new divisor 20 and the new remainder 15,and apply the division lemma to get
20 = 15 x 1 + 5
We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get
15 = 5 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 770 and 985 is 5
Notice that 5 = HCF(15,5) = HCF(20,15) = HCF(35,20) = HCF(90,35) = HCF(125,90) = HCF(215,125) = HCF(770,215) = HCF(985,770) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 270 > 5, we apply the division lemma to 270 and 5, to get
270 = 5 x 54 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 270 is 5
Notice that 5 = HCF(270,5) .
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, 985, 270?
Answer: HCF of 770, 985, 270 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 770, 985, 270 using Euclid's Algorithm?
Answer: For arbitrary numbers 770, 985, 270 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.