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 429, 727, 922 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 429, 727, 922 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 429, 727, 922 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 429, 727, 922 is 1.
HCF(429, 727, 922) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 429, 727, 922 is 1.
Step 1: Since 727 > 429, we apply the division lemma to 727 and 429, to get
727 = 429 x 1 + 298
Step 2: Since the reminder 429 ≠ 0, we apply division lemma to 298 and 429, to get
429 = 298 x 1 + 131
Step 3: We consider the new divisor 298 and the new remainder 131, and apply the division lemma to get
298 = 131 x 2 + 36
We consider the new divisor 131 and the new remainder 36,and apply the division lemma to get
131 = 36 x 3 + 23
We consider the new divisor 36 and the new remainder 23,and apply the division lemma to get
36 = 23 x 1 + 13
We consider the new divisor 23 and the new remainder 13,and apply the division lemma to get
23 = 13 x 1 + 10
We consider the new divisor 13 and the new remainder 10,and apply the division lemma to get
13 = 10 x 1 + 3
We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get
10 = 3 x 3 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 429 and 727 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(23,13) = HCF(36,23) = HCF(131,36) = HCF(298,131) = HCF(429,298) = HCF(727,429) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 922 > 1, we apply the division lemma to 922 and 1, to get
922 = 1 x 922 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 922 is 1
Notice that 1 = HCF(922,1) .
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 429, 727, 922?
Answer: HCF of 429, 727, 922 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 429, 727, 922 using Euclid's Algorithm?
Answer: For arbitrary numbers 429, 727, 922 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.