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 675, 497 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 675, 497 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 675, 497 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 675, 497 is 1.
HCF(675, 497) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 675, 497 is 1.
Step 1: Since 675 > 497, we apply the division lemma to 675 and 497, to get
675 = 497 x 1 + 178
Step 2: Since the reminder 497 ≠ 0, we apply division lemma to 178 and 497, to get
497 = 178 x 2 + 141
Step 3: We consider the new divisor 178 and the new remainder 141, and apply the division lemma to get
178 = 141 x 1 + 37
We consider the new divisor 141 and the new remainder 37,and apply the division lemma to get
141 = 37 x 3 + 30
We consider the new divisor 37 and the new remainder 30,and apply the division lemma to get
37 = 30 x 1 + 7
We consider the new divisor 30 and the new remainder 7,and apply the division lemma to get
30 = 7 x 4 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 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 675 and 497 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(30,7) = HCF(37,30) = HCF(141,37) = HCF(178,141) = HCF(497,178) = HCF(675,497) .
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 675, 497?
Answer: HCF of 675, 497 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 675, 497 using Euclid's Algorithm?
Answer: For arbitrary numbers 675, 497 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.