Highest Common Factor of 42, 30, 67, 520 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 42, 30, 67, 520 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 42, 30, 67, 520 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 42, 30, 67, 520 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 42, 30, 67, 520 is 1.
HCF(42, 30, 67, 520) = 1
HCF of 42, 30, 67, 520 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 42, 30, 67, 520 is 1.
Highest Common Factor of 42,30,67,520 is 1
Step 1: Since 42 > 30, we apply the division lemma to 42 and 30, to get
42 = 30 x 1 + 12
Step 2: Since the reminder 30 ≠ 0, we apply division lemma to 12 and 30, to get
30 = 12 x 2 + 6
Step 3: We consider the new divisor 12 and the new remainder 6, and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 42 and 30 is 6
Notice that 6 = HCF(12,6) = HCF(30,12) = HCF(42,30) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 67 > 6, we apply the division lemma to 67 and 6, to get
67 = 6 x 11 + 1
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 1 and 6, to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 67 is 1
Notice that 1 = HCF(6,1) = HCF(67,6) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 520 > 1, we apply the division lemma to 520 and 1, to get
520 = 1 x 520 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 520 is 1
Notice that 1 = HCF(520,1) .
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Frequently Asked Questions on HCF of 42, 30, 67, 520 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 42, 30, 67, 520?
Answer: HCF of 42, 30, 67, 520 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 42, 30, 67, 520 using Euclid's Algorithm?
Answer: For arbitrary numbers 42, 30, 67, 520 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.