Highest Common Factor of 120, 666, 703, 351 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, 666, 703, 351 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 120, 666, 703, 351 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, 666, 703, 351 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, 666, 703, 351 is 1.
HCF(120, 666, 703, 351) = 1
HCF of 120, 666, 703, 351 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, 666, 703, 351 is 1.
Highest Common Factor of 120,666,703,351 is 1
Step 1: Since 666 > 120, we apply the division lemma to 666 and 120, to get
666 = 120 x 5 + 66
Step 2: Since the reminder 120 ≠ 0, we apply division lemma to 66 and 120, to get
120 = 66 x 1 + 54
Step 3: We consider the new divisor 66 and the new remainder 54, and apply the division lemma to get
66 = 54 x 1 + 12
We consider the new divisor 54 and the new remainder 12,and apply the division lemma to get
54 = 12 x 4 + 6
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 120 and 666 is 6
Notice that 6 = HCF(12,6) = HCF(54,12) = HCF(66,54) = HCF(120,66) = HCF(666,120) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 703 > 6, we apply the division lemma to 703 and 6, to get
703 = 6 x 117 + 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 703 is 1
Notice that 1 = HCF(6,1) = HCF(703,6) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 351 > 1, we apply the division lemma to 351 and 1, to get
351 = 1 x 351 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 351 is 1
Notice that 1 = HCF(351,1) .
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Frequently Asked Questions on HCF of 120, 666, 703, 351 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, 666, 703, 351?
Answer: HCF of 120, 666, 703, 351 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 120, 666, 703, 351 using Euclid's Algorithm?
Answer: For arbitrary numbers 120, 666, 703, 351 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.