Highest Common Factor of 747, 120, 508 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 747, 120, 508 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 747, 120, 508 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 747, 120, 508 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 747, 120, 508 is 1.
HCF(747, 120, 508) = 1
HCF of 747, 120, 508 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 747, 120, 508 is 1.
Highest Common Factor of 747,120,508 is 1
Step 1: Since 747 > 120, we apply the division lemma to 747 and 120, to get
747 = 120 x 6 + 27
Step 2: Since the reminder 120 ≠ 0, we apply division lemma to 27 and 120, to get
120 = 27 x 4 + 12
Step 3: We consider the new divisor 27 and the new remainder 12, and apply the division lemma to get
27 = 12 x 2 + 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 747 and 120 is 3
Notice that 3 = HCF(12,3) = HCF(27,12) = HCF(120,27) = HCF(747,120) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 508 > 3, we apply the division lemma to 508 and 3, to get
508 = 3 x 169 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 508 is 1
Notice that 1 = HCF(3,1) = HCF(508,3) .
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Frequently Asked Questions on HCF of 747, 120, 508 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 747, 120, 508?
Answer: HCF of 747, 120, 508 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 747, 120, 508 using Euclid's Algorithm?
Answer: For arbitrary numbers 747, 120, 508 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.