Highest Common Factor of 990, 714, 686 using Euclid's algorithm
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 990, 714, 686 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 990, 714, 686 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 990, 714, 686 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 990, 714, 686 is 2.
HCF(990, 714, 686) = 2
HCF of 990, 714, 686 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 990, 714, 686 is 2.
Highest Common Factor of 990,714,686 is 2
Step 1: Since 990 > 714, we apply the division lemma to 990 and 714, to get
990 = 714 x 1 + 276
Step 2: Since the reminder 714 ≠ 0, we apply division lemma to 276 and 714, to get
714 = 276 x 2 + 162
Step 3: We consider the new divisor 276 and the new remainder 162, and apply the division lemma to get
276 = 162 x 1 + 114
We consider the new divisor 162 and the new remainder 114,and apply the division lemma to get
162 = 114 x 1 + 48
We consider the new divisor 114 and the new remainder 48,and apply the division lemma to get
114 = 48 x 2 + 18
We consider the new divisor 48 and the new remainder 18,and apply the division lemma to get
48 = 18 x 2 + 12
We consider the new divisor 18 and the new remainder 12,and apply the division lemma to get
18 = 12 x 1 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 990 and 714 is 6
Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(48,18) = HCF(114,48) = HCF(162,114) = HCF(276,162) = HCF(714,276) = HCF(990,714) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 686 > 6, we apply the division lemma to 686 and 6, to get
686 = 6 x 114 + 2
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 2 and 6, 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 6 and 686 is 2
Notice that 2 = HCF(6,2) = HCF(686,6) .
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Frequently Asked Questions on HCF of 990, 714, 686 using Euclid's Algorithm
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 990, 714, 686?
Answer: HCF of 990, 714, 686 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 990, 714, 686 using Euclid's Algorithm?
Answer: For arbitrary numbers 990, 714, 686 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.