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 723, 454 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 723, 454 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 723, 454 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 723, 454 is 1.
HCF(723, 454) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 723, 454 is 1.
Step 1: Since 723 > 454, we apply the division lemma to 723 and 454, to get
723 = 454 x 1 + 269
Step 2: Since the reminder 454 ≠ 0, we apply division lemma to 269 and 454, to get
454 = 269 x 1 + 185
Step 3: We consider the new divisor 269 and the new remainder 185, and apply the division lemma to get
269 = 185 x 1 + 84
We consider the new divisor 185 and the new remainder 84,and apply the division lemma to get
185 = 84 x 2 + 17
We consider the new divisor 84 and the new remainder 17,and apply the division lemma to get
84 = 17 x 4 + 16
We consider the new divisor 17 and the new remainder 16,and apply the division lemma to get
17 = 16 x 1 + 1
We consider the new divisor 16 and the new remainder 1,and apply the division lemma to get
16 = 1 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 723 and 454 is 1
Notice that 1 = HCF(16,1) = HCF(17,16) = HCF(84,17) = HCF(185,84) = HCF(269,185) = HCF(454,269) = HCF(723,454) .
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 723, 454?
Answer: HCF of 723, 454 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 723, 454 using Euclid's Algorithm?
Answer: For arbitrary numbers 723, 454 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.