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 495, 781, 921 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 495, 781, 921 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 495, 781, 921 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 495, 781, 921 is 1.
HCF(495, 781, 921) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 495, 781, 921 is 1.
Step 1: Since 781 > 495, we apply the division lemma to 781 and 495, to get
781 = 495 x 1 + 286
Step 2: Since the reminder 495 ≠ 0, we apply division lemma to 286 and 495, to get
495 = 286 x 1 + 209
Step 3: We consider the new divisor 286 and the new remainder 209, and apply the division lemma to get
286 = 209 x 1 + 77
We consider the new divisor 209 and the new remainder 77,and apply the division lemma to get
209 = 77 x 2 + 55
We consider the new divisor 77 and the new remainder 55,and apply the division lemma to get
77 = 55 x 1 + 22
We consider the new divisor 55 and the new remainder 22,and apply the division lemma to get
55 = 22 x 2 + 11
We consider the new divisor 22 and the new remainder 11,and apply the division lemma to get
22 = 11 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 495 and 781 is 11
Notice that 11 = HCF(22,11) = HCF(55,22) = HCF(77,55) = HCF(209,77) = HCF(286,209) = HCF(495,286) = HCF(781,495) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 921 > 11, we apply the division lemma to 921 and 11, to get
921 = 11 x 83 + 8
Step 2: Since the reminder 11 ≠ 0, we apply division lemma to 8 and 11, to get
11 = 8 x 1 + 3
Step 3: We consider the new divisor 8 and the new remainder 3, and apply the division lemma to get
8 = 3 x 2 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 11 and 921 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(921,11) .
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 495, 781, 921?
Answer: HCF of 495, 781, 921 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 495, 781, 921 using Euclid's Algorithm?
Answer: For arbitrary numbers 495, 781, 921 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.