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, 840, 321 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 714, 840, 321 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, 840, 321 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, 840, 321 is 3.
HCF(714, 840, 321) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 714, 840, 321 is 3.
Step 1: Since 840 > 714, we apply the division lemma to 840 and 714, to get
840 = 714 x 1 + 126
Step 2: Since the reminder 714 ≠ 0, we apply division lemma to 126 and 714, to get
714 = 126 x 5 + 84
Step 3: We consider the new divisor 126 and the new remainder 84, and apply the division lemma to get
126 = 84 x 1 + 42
We consider the new divisor 84 and the new remainder 42, and apply the division lemma to get
84 = 42 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 42, the HCF of 714 and 840 is 42
Notice that 42 = HCF(84,42) = HCF(126,84) = HCF(714,126) = HCF(840,714) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 321 > 42, we apply the division lemma to 321 and 42, to get
321 = 42 x 7 + 27
Step 2: Since the reminder 42 ≠ 0, we apply division lemma to 27 and 42, to get
42 = 27 x 1 + 15
Step 3: 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 42 and 321 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(27,15) = HCF(42,27) = HCF(321,42) .
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, 840, 321?
Answer: HCF of 714, 840, 321 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 714, 840, 321 using Euclid's Algorithm?
Answer: For arbitrary numbers 714, 840, 321 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.