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 273, 974, 651 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 273, 974, 651 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 273, 974, 651 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 273, 974, 651 is 1.
HCF(273, 974, 651) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 273, 974, 651 is 1.
Step 1: Since 974 > 273, we apply the division lemma to 974 and 273, to get
974 = 273 x 3 + 155
Step 2: Since the reminder 273 ≠ 0, we apply division lemma to 155 and 273, to get
273 = 155 x 1 + 118
Step 3: We consider the new divisor 155 and the new remainder 118, and apply the division lemma to get
155 = 118 x 1 + 37
We consider the new divisor 118 and the new remainder 37,and apply the division lemma to get
118 = 37 x 3 + 7
We consider the new divisor 37 and the new remainder 7,and apply the division lemma to get
37 = 7 x 5 + 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 273 and 974 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(37,7) = HCF(118,37) = HCF(155,118) = HCF(273,155) = HCF(974,273) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 651 > 1, we apply the division lemma to 651 and 1, to get
651 = 1 x 651 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 651 is 1
Notice that 1 = HCF(651,1) .
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 273, 974, 651?
Answer: HCF of 273, 974, 651 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 273, 974, 651 using Euclid's Algorithm?
Answer: For arbitrary numbers 273, 974, 651 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.