Highest Common Factor of 178, 458, 70 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 178, 458, 70 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 178, 458, 70 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 178, 458, 70 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 178, 458, 70 is 2.
HCF(178, 458, 70) = 2
HCF of 178, 458, 70 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 178, 458, 70 is 2.
Highest Common Factor of 178,458,70 is 2
Step 1: Since 458 > 178, we apply the division lemma to 458 and 178, to get
458 = 178 x 2 + 102
Step 2: Since the reminder 178 ≠ 0, we apply division lemma to 102 and 178, to get
178 = 102 x 1 + 76
Step 3: We consider the new divisor 102 and the new remainder 76, and apply the division lemma to get
102 = 76 x 1 + 26
We consider the new divisor 76 and the new remainder 26,and apply the division lemma to get
76 = 26 x 2 + 24
We consider the new divisor 26 and the new remainder 24,and apply the division lemma to get
26 = 24 x 1 + 2
We consider the new divisor 24 and the new remainder 2,and apply the division lemma to get
24 = 2 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 178 and 458 is 2
Notice that 2 = HCF(24,2) = HCF(26,24) = HCF(76,26) = HCF(102,76) = HCF(178,102) = HCF(458,178) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 70 > 2, we apply the division lemma to 70 and 2, to get
70 = 2 x 35 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 70 is 2
Notice that 2 = HCF(70,2) .
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Frequently Asked Questions on HCF of 178, 458, 70 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 178, 458, 70?
Answer: HCF of 178, 458, 70 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 178, 458, 70 using Euclid's Algorithm?
Answer: For arbitrary numbers 178, 458, 70 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.