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 714, 567, 600 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 714, 567, 600 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 714, 567, 600 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 714, 567, 600 is 3.
HCF(714, 567, 600) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 714, 567, 600 is 3.
Step 1: Since 714 > 567, we apply the division lemma to 714 and 567, to get
714 = 567 x 1 + 147
Step 2: Since the reminder 567 ≠ 0, we apply division lemma to 147 and 567, to get
567 = 147 x 3 + 126
Step 3: We consider the new divisor 147 and the new remainder 126, and apply the division lemma to get
147 = 126 x 1 + 21
We consider the new divisor 126 and the new remainder 21, and apply the division lemma to get
126 = 21 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 714 and 567 is 21
Notice that 21 = HCF(126,21) = HCF(147,126) = HCF(567,147) = HCF(714,567) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 600 > 21, we apply the division lemma to 600 and 21, to get
600 = 21 x 28 + 12
Step 2: Since the reminder 21 ≠ 0, we apply division lemma to 12 and 21, to get
21 = 12 x 1 + 9
Step 3: We consider the new divisor 12 and the new remainder 9, and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3, and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 21 and 600 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(600,21) .
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 714, 567, 600?
Answer: HCF of 714, 567, 600 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 714, 567, 600 using Euclid's Algorithm?
Answer: For arbitrary numbers 714, 567, 600 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.