Highest Common Factor of 990, 712 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, 712 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 990, 712 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, 712 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, 712 is 2.
HCF(990, 712) = 2
HCF of 990, 712 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, 712 is 2.
Highest Common Factor of 990,712 is 2
Step 1: Since 990 > 712, we apply the division lemma to 990 and 712, to get
990 = 712 x 1 + 278
Step 2: Since the reminder 712 ≠ 0, we apply division lemma to 278 and 712, to get
712 = 278 x 2 + 156
Step 3: We consider the new divisor 278 and the new remainder 156, and apply the division lemma to get
278 = 156 x 1 + 122
We consider the new divisor 156 and the new remainder 122,and apply the division lemma to get
156 = 122 x 1 + 34
We consider the new divisor 122 and the new remainder 34,and apply the division lemma to get
122 = 34 x 3 + 20
We consider the new divisor 34 and the new remainder 20,and apply the division lemma to get
34 = 20 x 1 + 14
We consider the new divisor 20 and the new remainder 14,and apply the division lemma to get
20 = 14 x 1 + 6
We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get
14 = 6 x 2 + 2
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 990 and 712 is 2
Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(20,14) = HCF(34,20) = HCF(122,34) = HCF(156,122) = HCF(278,156) = HCF(712,278) = HCF(990,712) .
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Frequently Asked Questions on HCF of 990, 712 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, 712?
Answer: HCF of 990, 712 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 990, 712 using Euclid's Algorithm?
Answer: For arbitrary numbers 990, 712 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.