Highest Common Factor of 70, 182, 623 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 70, 182, 623 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 70, 182, 623 is 7 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 70, 182, 623 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 70, 182, 623 is 7.
HCF(70, 182, 623) = 7
HCF of 70, 182, 623 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 70, 182, 623 is 7.
Highest Common Factor of 70,182,623 is 7
Step 1: Since 182 > 70, we apply the division lemma to 182 and 70, to get
182 = 70 x 2 + 42
Step 2: Since the reminder 70 ≠ 0, we apply division lemma to 42 and 70, to get
70 = 42 x 1 + 28
Step 3: We consider the new divisor 42 and the new remainder 28, and apply the division lemma to get
42 = 28 x 1 + 14
We consider the new divisor 28 and the new remainder 14, and apply the division lemma to get
28 = 14 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 70 and 182 is 14
Notice that 14 = HCF(28,14) = HCF(42,28) = HCF(70,42) = HCF(182,70) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 623 > 14, we apply the division lemma to 623 and 14, to get
623 = 14 x 44 + 7
Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 7 and 14, to get
14 = 7 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 14 and 623 is 7
Notice that 7 = HCF(14,7) = HCF(623,14) .
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Frequently Asked Questions on HCF of 70, 182, 623 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 70, 182, 623?
Answer: HCF of 70, 182, 623 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 70, 182, 623 using Euclid's Algorithm?
Answer: For arbitrary numbers 70, 182, 623 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
