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 471, 774 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 471, 774 is 3 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 471, 774 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 471, 774 is 3.
HCF(471, 774) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 471, 774 is 3.
Step 1: Since 774 > 471, we apply the division lemma to 774 and 471, to get
774 = 471 x 1 + 303
Step 2: Since the reminder 471 ≠ 0, we apply division lemma to 303 and 471, to get
471 = 303 x 1 + 168
Step 3: We consider the new divisor 303 and the new remainder 168, and apply the division lemma to get
303 = 168 x 1 + 135
We consider the new divisor 168 and the new remainder 135,and apply the division lemma to get
168 = 135 x 1 + 33
We consider the new divisor 135 and the new remainder 33,and apply the division lemma to get
135 = 33 x 4 + 3
We consider the new divisor 33 and the new remainder 3,and apply the division lemma to get
33 = 3 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 471 and 774 is 3
Notice that 3 = HCF(33,3) = HCF(135,33) = HCF(168,135) = HCF(303,168) = HCF(471,303) = HCF(774,471) .
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 471, 774?
Answer: HCF of 471, 774 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 471, 774 using Euclid's Algorithm?
Answer: For arbitrary numbers 471, 774 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.