Highest Common Factor of 766, 990 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 766, 990 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 766, 990 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 766, 990 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 766, 990 is 2.
HCF(766, 990) = 2
HCF of 766, 990 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 766, 990 is 2.
Highest Common Factor of 766,990 is 2
Step 1: Since 990 > 766, we apply the division lemma to 990 and 766, to get
990 = 766 x 1 + 224
Step 2: Since the reminder 766 ≠ 0, we apply division lemma to 224 and 766, to get
766 = 224 x 3 + 94
Step 3: We consider the new divisor 224 and the new remainder 94, and apply the division lemma to get
224 = 94 x 2 + 36
We consider the new divisor 94 and the new remainder 36,and apply the division lemma to get
94 = 36 x 2 + 22
We consider the new divisor 36 and the new remainder 22,and apply the division lemma to get
36 = 22 x 1 + 14
We consider the new divisor 22 and the new remainder 14,and apply the division lemma to get
22 = 14 x 1 + 8
We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get
14 = 8 x 1 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 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 766 and 990 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(22,14) = HCF(36,22) = HCF(94,36) = HCF(224,94) = HCF(766,224) = HCF(990,766) .
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Frequently Asked Questions on HCF of 766, 990 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 766, 990?
Answer: HCF of 766, 990 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 766, 990 using Euclid's Algorithm?
Answer: For arbitrary numbers 766, 990 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.