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 455, 690, 777, 471 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 455, 690, 777, 471 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 455, 690, 777, 471 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 455, 690, 777, 471 is 1.
HCF(455, 690, 777, 471) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 455, 690, 777, 471 is 1.
Step 1: Since 690 > 455, we apply the division lemma to 690 and 455, to get
690 = 455 x 1 + 235
Step 2: Since the reminder 455 ≠ 0, we apply division lemma to 235 and 455, to get
455 = 235 x 1 + 220
Step 3: We consider the new divisor 235 and the new remainder 220, and apply the division lemma to get
235 = 220 x 1 + 15
We consider the new divisor 220 and the new remainder 15,and apply the division lemma to get
220 = 15 x 14 + 10
We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get
15 = 10 x 1 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 455 and 690 is 5
Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(220,15) = HCF(235,220) = HCF(455,235) = HCF(690,455) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 777 > 5, we apply the division lemma to 777 and 5, to get
777 = 5 x 155 + 2
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 2 and 5, to get
5 = 2 x 2 + 1
Step 3: 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 5 and 777 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(777,5) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 471 > 1, we apply the division lemma to 471 and 1, to get
471 = 1 x 471 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 471 is 1
Notice that 1 = HCF(471,1) .
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 455, 690, 777, 471?
Answer: HCF of 455, 690, 777, 471 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 455, 690, 777, 471 using Euclid's Algorithm?
Answer: For arbitrary numbers 455, 690, 777, 471 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.