Highest Common Factor of 351, 975, 45 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 351, 975, 45 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 351, 975, 45 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 351, 975, 45 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 351, 975, 45 is 3.
HCF(351, 975, 45) = 3
HCF of 351, 975, 45 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 351, 975, 45 is 3.
Highest Common Factor of 351,975,45 is 3
Step 1: Since 975 > 351, we apply the division lemma to 975 and 351, to get
975 = 351 x 2 + 273
Step 2: Since the reminder 351 ≠ 0, we apply division lemma to 273 and 351, to get
351 = 273 x 1 + 78
Step 3: We consider the new divisor 273 and the new remainder 78, and apply the division lemma to get
273 = 78 x 3 + 39
We consider the new divisor 78 and the new remainder 39, and apply the division lemma to get
78 = 39 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 39, the HCF of 351 and 975 is 39
Notice that 39 = HCF(78,39) = HCF(273,78) = HCF(351,273) = HCF(975,351) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 45 > 39, we apply the division lemma to 45 and 39, to get
45 = 39 x 1 + 6
Step 2: Since the reminder 39 ≠ 0, we apply division lemma to 6 and 39, to get
39 = 6 x 6 + 3
Step 3: We consider the new divisor 6 and the new remainder 3, and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 39 and 45 is 3
Notice that 3 = HCF(6,3) = HCF(39,6) = HCF(45,39) .
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Frequently Asked Questions on HCF of 351, 975, 45 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 351, 975, 45?
Answer: HCF of 351, 975, 45 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 351, 975, 45 using Euclid's Algorithm?
Answer: For arbitrary numbers 351, 975, 45 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.