Highest Common Factor of 474, 652, 142, 14 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 474, 652, 142, 14 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 474, 652, 142, 14 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 474, 652, 142, 14 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 474, 652, 142, 14 is 2.
HCF(474, 652, 142, 14) = 2
HCF of 474, 652, 142, 14 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 474, 652, 142, 14 is 2.
Highest Common Factor of 474,652,142,14 is 2
Step 1: Since 652 > 474, we apply the division lemma to 652 and 474, to get
652 = 474 x 1 + 178
Step 2: Since the reminder 474 ≠ 0, we apply division lemma to 178 and 474, to get
474 = 178 x 2 + 118
Step 3: We consider the new divisor 178 and the new remainder 118, and apply the division lemma to get
178 = 118 x 1 + 60
We consider the new divisor 118 and the new remainder 60,and apply the division lemma to get
118 = 60 x 1 + 58
We consider the new divisor 60 and the new remainder 58,and apply the division lemma to get
60 = 58 x 1 + 2
We consider the new divisor 58 and the new remainder 2,and apply the division lemma to get
58 = 2 x 29 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 474 and 652 is 2
Notice that 2 = HCF(58,2) = HCF(60,58) = HCF(118,60) = HCF(178,118) = HCF(474,178) = HCF(652,474) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 142 > 2, we apply the division lemma to 142 and 2, to get
142 = 2 x 71 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 142 is 2
Notice that 2 = HCF(142,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 14 > 2, we apply the division lemma to 14 and 2, to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 14 is 2
Notice that 2 = HCF(14,2) .
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Frequently Asked Questions on HCF of 474, 652, 142, 14 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 474, 652, 142, 14?
Answer: HCF of 474, 652, 142, 14 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 474, 652, 142, 14 using Euclid's Algorithm?
Answer: For arbitrary numbers 474, 652, 142, 14 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.