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 654, 807, 717 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 654, 807, 717 is 3 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 654, 807, 717 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 654, 807, 717 is 3.
HCF(654, 807, 717) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 654, 807, 717 is 3.
Step 1: Since 807 > 654, we apply the division lemma to 807 and 654, to get
807 = 654 x 1 + 153
Step 2: Since the reminder 654 ≠ 0, we apply division lemma to 153 and 654, to get
654 = 153 x 4 + 42
Step 3: We consider the new divisor 153 and the new remainder 42, and apply the division lemma to get
153 = 42 x 3 + 27
We consider the new divisor 42 and the new remainder 27,and apply the division lemma to get
42 = 27 x 1 + 15
We consider the new divisor 27 and the new remainder 15,and apply the division lemma to get
27 = 15 x 1 + 12
We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get
15 = 12 x 1 + 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 654 and 807 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(27,15) = HCF(42,27) = HCF(153,42) = HCF(654,153) = HCF(807,654) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 717 > 3, we apply the division lemma to 717 and 3, to get
717 = 3 x 239 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 717 is 3
Notice that 3 = HCF(717,3) .
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 654, 807, 717?
Answer: HCF of 654, 807, 717 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 654, 807, 717 using Euclid's Algorithm?
Answer: For arbitrary numbers 654, 807, 717 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.