Highest Common Factor of 990, 178 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, 178 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 990, 178 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, 178 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, 178 is 2.
HCF(990, 178) = 2
HCF of 990, 178 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, 178 is 2.
Highest Common Factor of 990,178 is 2
Step 1: Since 990 > 178, we apply the division lemma to 990 and 178, to get
990 = 178 x 5 + 100
Step 2: Since the reminder 178 ≠ 0, we apply division lemma to 100 and 178, to get
178 = 100 x 1 + 78
Step 3: We consider the new divisor 100 and the new remainder 78, and apply the division lemma to get
100 = 78 x 1 + 22
We consider the new divisor 78 and the new remainder 22,and apply the division lemma to get
78 = 22 x 3 + 12
We consider the new divisor 22 and the new remainder 12,and apply the division lemma to get
22 = 12 x 1 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 990 and 178 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(22,12) = HCF(78,22) = HCF(100,78) = HCF(178,100) = HCF(990,178) .
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Frequently Asked Questions on HCF of 990, 178 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, 178?
Answer: HCF of 990, 178 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 990, 178 using Euclid's Algorithm?
Answer: For arbitrary numbers 990, 178 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.