Highest Common Factor of 75, 351, 802 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 75, 351, 802 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 75, 351, 802 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 75, 351, 802 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 75, 351, 802 is 1.
HCF(75, 351, 802) = 1
HCF of 75, 351, 802 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 75, 351, 802 is 1.
Highest Common Factor of 75,351,802 is 1
Step 1: Since 351 > 75, we apply the division lemma to 351 and 75, to get
351 = 75 x 4 + 51
Step 2: Since the reminder 75 ≠ 0, we apply division lemma to 51 and 75, to get
75 = 51 x 1 + 24
Step 3: We consider the new divisor 51 and the new remainder 24, and apply the division lemma to get
51 = 24 x 2 + 3
We consider the new divisor 24 and the new remainder 3, and apply the division lemma to get
24 = 3 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 75 and 351 is 3
Notice that 3 = HCF(24,3) = HCF(51,24) = HCF(75,51) = HCF(351,75) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 802 > 3, we apply the division lemma to 802 and 3, to get
802 = 3 x 267 + 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 802 is 1
Notice that 1 = HCF(3,1) = HCF(802,3) .
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Frequently Asked Questions on HCF of 75, 351, 802 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 75, 351, 802?
Answer: HCF of 75, 351, 802 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 75, 351, 802 using Euclid's Algorithm?
Answer: For arbitrary numbers 75, 351, 802 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.