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 975, 635 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 975, 635 is 5 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 975, 635 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 975, 635 is 5.
HCF(975, 635) = 5
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 975, 635 is 5.
Step 1: Since 975 > 635, we apply the division lemma to 975 and 635, to get
975 = 635 x 1 + 340
Step 2: Since the reminder 635 ≠ 0, we apply division lemma to 340 and 635, to get
635 = 340 x 1 + 295
Step 3: We consider the new divisor 340 and the new remainder 295, and apply the division lemma to get
340 = 295 x 1 + 45
We consider the new divisor 295 and the new remainder 45,and apply the division lemma to get
295 = 45 x 6 + 25
We consider the new divisor 45 and the new remainder 25,and apply the division lemma to get
45 = 25 x 1 + 20
We consider the new divisor 25 and the new remainder 20,and apply the division lemma to get
25 = 20 x 1 + 5
We consider the new divisor 20 and the new remainder 5,and apply the division lemma to get
20 = 5 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 975 and 635 is 5
Notice that 5 = HCF(20,5) = HCF(25,20) = HCF(45,25) = HCF(295,45) = HCF(340,295) = HCF(635,340) = HCF(975,635) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 975, 635?
Answer: HCF of 975, 635 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 975, 635 using Euclid's Algorithm?
Answer: For arbitrary numbers 975, 635 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.