Highest Common Factor of 994, 634, 990, 174 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 994, 634, 990, 174 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 994, 634, 990, 174 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 994, 634, 990, 174 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 994, 634, 990, 174 is 2.
HCF(994, 634, 990, 174) = 2
HCF of 994, 634, 990, 174 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 994, 634, 990, 174 is 2.
Highest Common Factor of 994,634,990,174 is 2
Step 1: Since 994 > 634, we apply the division lemma to 994 and 634, to get
994 = 634 x 1 + 360
Step 2: Since the reminder 634 ≠ 0, we apply division lemma to 360 and 634, to get
634 = 360 x 1 + 274
Step 3: We consider the new divisor 360 and the new remainder 274, and apply the division lemma to get
360 = 274 x 1 + 86
We consider the new divisor 274 and the new remainder 86,and apply the division lemma to get
274 = 86 x 3 + 16
We consider the new divisor 86 and the new remainder 16,and apply the division lemma to get
86 = 16 x 5 + 6
We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get
16 = 6 x 2 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 994 and 634 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(86,16) = HCF(274,86) = HCF(360,274) = HCF(634,360) = HCF(994,634) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 990 > 2, we apply the division lemma to 990 and 2, to get
990 = 2 x 495 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 990 is 2
Notice that 2 = HCF(990,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 174 > 2, we apply the division lemma to 174 and 2, to get
174 = 2 x 87 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 174 is 2
Notice that 2 = HCF(174,2) .
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Frequently Asked Questions on HCF of 994, 634, 990, 174 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 994, 634, 990, 174?
Answer: HCF of 994, 634, 990, 174 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 994, 634, 990, 174 using Euclid's Algorithm?
Answer: For arbitrary numbers 994, 634, 990, 174 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.