Highest Common Factor of 420, 970, 132, 551 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 420, 970, 132, 551 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 420, 970, 132, 551 is 1 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 420, 970, 132, 551 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 420, 970, 132, 551 is 1.
HCF(420, 970, 132, 551) = 1
HCF of 420, 970, 132, 551 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 420, 970, 132, 551 is 1.
Highest Common Factor of 420,970,132,551 is 1
Step 1: Since 970 > 420, we apply the division lemma to 970 and 420, to get
970 = 420 x 2 + 130
Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 130 and 420, to get
420 = 130 x 3 + 30
Step 3: We consider the new divisor 130 and the new remainder 30, and apply the division lemma to get
130 = 30 x 4 + 10
We consider the new divisor 30 and the new remainder 10, and apply the division lemma to get
30 = 10 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 420 and 970 is 10
Notice that 10 = HCF(30,10) = HCF(130,30) = HCF(420,130) = HCF(970,420) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 132 > 10, we apply the division lemma to 132 and 10, to get
132 = 10 x 13 + 2
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 2 and 10, to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 10 and 132 is 2
Notice that 2 = HCF(10,2) = HCF(132,10) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 551 > 2, we apply the division lemma to 551 and 2, to get
551 = 2 x 275 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 551 is 1
Notice that 1 = HCF(2,1) = HCF(551,2) .
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Frequently Asked Questions on HCF of 420, 970, 132, 551 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 420, 970, 132, 551?
Answer: HCF of 420, 970, 132, 551 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 420, 970, 132, 551 using Euclid's Algorithm?
Answer: For arbitrary numbers 420, 970, 132, 551 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.