Highest Common Factor of 120, 677, 542 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 120, 677, 542 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 120, 677, 542 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 120, 677, 542 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 120, 677, 542 is 1.
HCF(120, 677, 542) = 1
HCF of 120, 677, 542 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 120, 677, 542 is 1.
Highest Common Factor of 120,677,542 is 1
Step 1: Since 677 > 120, we apply the division lemma to 677 and 120, to get
677 = 120 x 5 + 77
Step 2: Since the reminder 120 ≠ 0, we apply division lemma to 77 and 120, to get
120 = 77 x 1 + 43
Step 3: We consider the new divisor 77 and the new remainder 43, and apply the division lemma to get
77 = 43 x 1 + 34
We consider the new divisor 43 and the new remainder 34,and apply the division lemma to get
43 = 34 x 1 + 9
We consider the new divisor 34 and the new remainder 9,and apply the division lemma to get
34 = 9 x 3 + 7
We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get
9 = 7 x 1 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 120 and 677 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(34,9) = HCF(43,34) = HCF(77,43) = HCF(120,77) = HCF(677,120) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 542 > 1, we apply the division lemma to 542 and 1, to get
542 = 1 x 542 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 542 is 1
Notice that 1 = HCF(542,1) .
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Frequently Asked Questions on HCF of 120, 677, 542 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 120, 677, 542?
Answer: HCF of 120, 677, 542 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 120, 677, 542 using Euclid's Algorithm?
Answer: For arbitrary numbers 120, 677, 542 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.