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 822, 497, 74 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 822, 497, 74 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 822, 497, 74 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 822, 497, 74 is 1.
HCF(822, 497, 74) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 822, 497, 74 is 1.
Step 1: Since 822 > 497, we apply the division lemma to 822 and 497, to get
822 = 497 x 1 + 325
Step 2: Since the reminder 497 ≠ 0, we apply division lemma to 325 and 497, to get
497 = 325 x 1 + 172
Step 3: We consider the new divisor 325 and the new remainder 172, and apply the division lemma to get
325 = 172 x 1 + 153
We consider the new divisor 172 and the new remainder 153,and apply the division lemma to get
172 = 153 x 1 + 19
We consider the new divisor 153 and the new remainder 19,and apply the division lemma to get
153 = 19 x 8 + 1
We consider the new divisor 19 and the new remainder 1,and apply the division lemma to get
19 = 1 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 822 and 497 is 1
Notice that 1 = HCF(19,1) = HCF(153,19) = HCF(172,153) = HCF(325,172) = HCF(497,325) = HCF(822,497) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 74 > 1, we apply the division lemma to 74 and 1, to get
74 = 1 x 74 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 74 is 1
Notice that 1 = HCF(74,1) .
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 822, 497, 74?
Answer: HCF of 822, 497, 74 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 822, 497, 74 using Euclid's Algorithm?
Answer: For arbitrary numbers 822, 497, 74 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.