Highest Common Factor of 555, 210, 42 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 555, 210, 42 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 555, 210, 42 is 3 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 555, 210, 42 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 555, 210, 42 is 3.
HCF(555, 210, 42) = 3
HCF of 555, 210, 42 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 555, 210, 42 is 3.
Highest Common Factor of 555,210,42 is 3
Step 1: Since 555 > 210, we apply the division lemma to 555 and 210, to get
555 = 210 x 2 + 135
Step 2: Since the reminder 210 ≠ 0, we apply division lemma to 135 and 210, to get
210 = 135 x 1 + 75
Step 3: We consider the new divisor 135 and the new remainder 75, and apply the division lemma to get
135 = 75 x 1 + 60
We consider the new divisor 75 and the new remainder 60,and apply the division lemma to get
75 = 60 x 1 + 15
We consider the new divisor 60 and the new remainder 15,and apply the division lemma to get
60 = 15 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 555 and 210 is 15
Notice that 15 = HCF(60,15) = HCF(75,60) = HCF(135,75) = HCF(210,135) = HCF(555,210) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 42 > 15, we apply the division lemma to 42 and 15, to get
42 = 15 x 2 + 12
Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 12 and 15, to get
15 = 12 x 1 + 3
Step 3: We consider the new divisor 12 and the new remainder 3, and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 15 and 42 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(42,15) .
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Frequently Asked Questions on HCF of 555, 210, 42 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 555, 210, 42?
Answer: HCF of 555, 210, 42 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 555, 210, 42 using Euclid's Algorithm?
Answer: For arbitrary numbers 555, 210, 42 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.