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 546, 825, 65 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 546, 825, 65 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 546, 825, 65 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 546, 825, 65 is 1.
HCF(546, 825, 65) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 546, 825, 65 is 1.
Step 1: Since 825 > 546, we apply the division lemma to 825 and 546, to get
825 = 546 x 1 + 279
Step 2: Since the reminder 546 ≠ 0, we apply division lemma to 279 and 546, to get
546 = 279 x 1 + 267
Step 3: We consider the new divisor 279 and the new remainder 267, and apply the division lemma to get
279 = 267 x 1 + 12
We consider the new divisor 267 and the new remainder 12,and apply the division lemma to get
267 = 12 x 22 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 546 and 825 is 3
Notice that 3 = HCF(12,3) = HCF(267,12) = HCF(279,267) = HCF(546,279) = HCF(825,546) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 65 > 3, we apply the division lemma to 65 and 3, to get
65 = 3 x 21 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 65 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(65,3) .
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 546, 825, 65?
Answer: HCF of 546, 825, 65 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 546, 825, 65 using Euclid's Algorithm?
Answer: For arbitrary numbers 546, 825, 65 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.