Highest Common Factor of 340, 935, 977 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 340, 935, 977 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 340, 935, 977 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 340, 935, 977 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 340, 935, 977 is 1.
HCF(340, 935, 977) = 1
HCF of 340, 935, 977 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 340, 935, 977 is 1.
Highest Common Factor of 340,935,977 is 1
Step 1: Since 935 > 340, we apply the division lemma to 935 and 340, to get
935 = 340 x 2 + 255
Step 2: Since the reminder 340 ≠ 0, we apply division lemma to 255 and 340, to get
340 = 255 x 1 + 85
Step 3: We consider the new divisor 255 and the new remainder 85, and apply the division lemma to get
255 = 85 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 85, the HCF of 340 and 935 is 85
Notice that 85 = HCF(255,85) = HCF(340,255) = HCF(935,340) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 977 > 85, we apply the division lemma to 977 and 85, to get
977 = 85 x 11 + 42
Step 2: Since the reminder 85 ≠ 0, we apply division lemma to 42 and 85, to get
85 = 42 x 2 + 1
Step 3: We consider the new divisor 42 and the new remainder 1, and apply the division lemma to get
42 = 1 x 42 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 85 and 977 is 1
Notice that 1 = HCF(42,1) = HCF(85,42) = HCF(977,85) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 340, 935, 977 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 340, 935, 977?
Answer: HCF of 340, 935, 977 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 340, 935, 977 using Euclid's Algorithm?
Answer: For arbitrary numbers 340, 935, 977 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.