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 826, 540, 435 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 826, 540, 435 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 826, 540, 435 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 826, 540, 435 is 1.
HCF(826, 540, 435) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 826, 540, 435 is 1.
Step 1: Since 826 > 540, we apply the division lemma to 826 and 540, to get
826 = 540 x 1 + 286
Step 2: Since the reminder 540 ≠ 0, we apply division lemma to 286 and 540, to get
540 = 286 x 1 + 254
Step 3: We consider the new divisor 286 and the new remainder 254, and apply the division lemma to get
286 = 254 x 1 + 32
We consider the new divisor 254 and the new remainder 32,and apply the division lemma to get
254 = 32 x 7 + 30
We consider the new divisor 32 and the new remainder 30,and apply the division lemma to get
32 = 30 x 1 + 2
We consider the new divisor 30 and the new remainder 2,and apply the division lemma to get
30 = 2 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 826 and 540 is 2
Notice that 2 = HCF(30,2) = HCF(32,30) = HCF(254,32) = HCF(286,254) = HCF(540,286) = HCF(826,540) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 435 > 2, we apply the division lemma to 435 and 2, to get
435 = 2 x 217 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 435 is 1
Notice that 1 = HCF(2,1) = HCF(435,2) .
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 826, 540, 435?
Answer: HCF of 826, 540, 435 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 826, 540, 435 using Euclid's Algorithm?
Answer: For arbitrary numbers 826, 540, 435 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.