Highest Common Factor of 670, 945, 187 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 670, 945, 187 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 670, 945, 187 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 670, 945, 187 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 670, 945, 187 is 1.
HCF(670, 945, 187) = 1
HCF of 670, 945, 187 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 670, 945, 187 is 1.
Highest Common Factor of 670,945,187 is 1
Step 1: Since 945 > 670, we apply the division lemma to 945 and 670, to get
945 = 670 x 1 + 275
Step 2: Since the reminder 670 ≠ 0, we apply division lemma to 275 and 670, to get
670 = 275 x 2 + 120
Step 3: We consider the new divisor 275 and the new remainder 120, and apply the division lemma to get
275 = 120 x 2 + 35
We consider the new divisor 120 and the new remainder 35,and apply the division lemma to get
120 = 35 x 3 + 15
We consider the new divisor 35 and the new remainder 15,and apply the division lemma to get
35 = 15 x 2 + 5
We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get
15 = 5 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 670 and 945 is 5
Notice that 5 = HCF(15,5) = HCF(35,15) = HCF(120,35) = HCF(275,120) = HCF(670,275) = HCF(945,670) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 187 > 5, we apply the division lemma to 187 and 5, to get
187 = 5 x 37 + 2
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 2 and 5, to get
5 = 2 x 2 + 1
Step 3: 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 5 and 187 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(187,5) .
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Frequently Asked Questions on HCF of 670, 945, 187 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 670, 945, 187?
Answer: HCF of 670, 945, 187 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 670, 945, 187 using Euclid's Algorithm?
Answer: For arbitrary numbers 670, 945, 187 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
