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 286, 390, 708 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 286, 390, 708 is 2 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 286, 390, 708 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 286, 390, 708 is 2.
HCF(286, 390, 708) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 286, 390, 708 is 2.
Step 1: Since 390 > 286, we apply the division lemma to 390 and 286, to get
390 = 286 x 1 + 104
Step 2: Since the reminder 286 ≠ 0, we apply division lemma to 104 and 286, to get
286 = 104 x 2 + 78
Step 3: We consider the new divisor 104 and the new remainder 78, and apply the division lemma to get
104 = 78 x 1 + 26
We consider the new divisor 78 and the new remainder 26, and apply the division lemma to get
78 = 26 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 26, the HCF of 286 and 390 is 26
Notice that 26 = HCF(78,26) = HCF(104,78) = HCF(286,104) = HCF(390,286) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 708 > 26, we apply the division lemma to 708 and 26, to get
708 = 26 x 27 + 6
Step 2: Since the reminder 26 ≠ 0, we apply division lemma to 6 and 26, to get
26 = 6 x 4 + 2
Step 3: We consider the new divisor 6 and the new remainder 2, and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 26 and 708 is 2
Notice that 2 = HCF(6,2) = HCF(26,6) = HCF(708,26) .
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 286, 390, 708?
Answer: HCF of 286, 390, 708 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 286, 390, 708 using Euclid's Algorithm?
Answer: For arbitrary numbers 286, 390, 708 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.