Highest Common Factor of 998, 696, 152 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 998, 696, 152 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 998, 696, 152 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 998, 696, 152 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 998, 696, 152 is 2.
HCF(998, 696, 152) = 2
HCF of 998, 696, 152 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 998, 696, 152 is 2.
Highest Common Factor of 998,696,152 is 2
Step 1: Since 998 > 696, we apply the division lemma to 998 and 696, to get
998 = 696 x 1 + 302
Step 2: Since the reminder 696 ≠ 0, we apply division lemma to 302 and 696, to get
696 = 302 x 2 + 92
Step 3: We consider the new divisor 302 and the new remainder 92, and apply the division lemma to get
302 = 92 x 3 + 26
We consider the new divisor 92 and the new remainder 26,and apply the division lemma to get
92 = 26 x 3 + 14
We consider the new divisor 26 and the new remainder 14,and apply the division lemma to get
26 = 14 x 1 + 12
We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get
14 = 12 x 1 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 998 and 696 is 2
Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(26,14) = HCF(92,26) = HCF(302,92) = HCF(696,302) = HCF(998,696) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 152 > 2, we apply the division lemma to 152 and 2, to get
152 = 2 x 76 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 152 is 2
Notice that 2 = HCF(152,2) .
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Frequently Asked Questions on HCF of 998, 696, 152 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 998, 696, 152?
Answer: HCF of 998, 696, 152 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 998, 696, 152 using Euclid's Algorithm?
Answer: For arbitrary numbers 998, 696, 152 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.